Theorem 19.31v

Description: Version of 19.31 with a disjoint variable condition, requiring fewer axioms. (Contributed by BJ, 7-Mar-2020)

	Ref	Expression
Assertion	19.31v	|- ( A. x ( ph \/ ps ) <-> ( A. x ph \/ ps ) )

Proof

Step	Hyp	Ref	Expression
1		19.32v	|- ( A. x ( ps \/ ph ) <-> ( ps \/ A. x ph ) )
2		orcom	|- ( ( ph \/ ps ) <-> ( ps \/ ph ) )
3	2	albii	|- ( A. x ( ph \/ ps ) <-> A. x ( ps \/ ph ) )
4		orcom	|- ( ( A. x ph \/ ps ) <-> ( ps \/ A. x ph ) )
5	1 3 4	3bitr4i	|- ( A. x ( ph \/ ps ) <-> ( A. x ph \/ ps ) )