Theorem 19.45v

Description: Version of 19.45 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Assertion	19.45v	|- ( E. x ( ph \/ ps ) <-> ( ph \/ E. x ps ) )

Proof

Step	Hyp	Ref	Expression
1		19.43	|- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
2		19.9v	|- ( E. x ph <-> ph )
3	2	orbi1i	|- ( ( E. x ph \/ E. x ps ) <-> ( ph \/ E. x ps ) )
4	1 3	bitri	|- ( E. x ( ph \/ ps ) <-> ( ph \/ E. x ps ) )