How do Comma-separated expressions as condition in a for-loop work?

I´ve seen a a few times already in answers and questions here on Stack Overflow, a comma-separated list as loop condition for a for-loop like : for(int i = 0, int j = 0 ; i < 2, j < 4; i++, j++) { ... }
. How does this work?

How does a comma-separated condition work in a for-loop in C?
Like:
for(int i = 0, int j = 1 ; i < 5, j < 4; i++, j++) { ... }

Isn´t this invalid because the condition needs to be an evaluated expression? How do the multiple comma-separated expressions get evaluated to one expression in the for-loop?

The mentioned expressions are enclosed by semicolons ; i < 5, j < 4;, and this shall be the condition of the loop. Or am I wrong?

The syntax for a for loop with a declaration is (6.8.5):

for ( declaration expression_opt ; expression_opt ) statement

This

for(int i = 0, int j = 1 ; i < 5, j < 4; i++, j++) { }

doesn't parse because

int i = 0, int j = 1 ; isn't syntactically valid as a declaration (or any sentential form in C for that matter) but

for(int i = 0, j = 1; i < 5, j < 4; i++, j++) { }

would parse, because

int i = 0, j = 1;

is a valid declaration (with multiple, initializer-containing declarators) and

i < 5, j < 4

is a valid comma-operator-containing expression, as is

i++, j++

.

(Note that i < 5, j < 4 has the same effect as just j < 4 because comma expressions are evaluated left to right and the value of the final part is used, and since i < 5 has no side-effect here, the whole expression is equivalent to just j < 4. You might have wanted i < 5 && j < 4 instead.)

In the original form of the for loop (without a declaration) you have (6.8.5)

 for ( expression_opt ; expression_opt ; expression_opt ) statement

and the semicolons are used to separate the 3 (optional) expressions.

In the declaration-containing form, the first semicolon is parsed as part of the declaration

for ( declaration expression_opt ; expression_opt ) statement

.

All the expressions in the comma-separated list are evaluated, but only the last expression is used for the for loop condition. So in effect the i<5 condition is ignored, since it's not the last expression.