Theorem 19.21vv

Description: Compare Theorem *11.3 in WhiteheadRussell p. 161. Special case of theorem 19.21 of Margaris p. 90 with two quantifiers. See 19.21v . (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	19.21vv	|- ( A. x A. y ( ps -> ph ) <-> ( ps -> A. x A. y ph ) )

Proof

Step	Hyp	Ref	Expression
1		19.21v	|- ( A. y ( ps -> ph ) <-> ( ps -> A. y ph ) )
2	1	albii	|- ( A. x A. y ( ps -> ph ) <-> A. x ( ps -> A. y ph ) )
3		19.21v	|- ( A. x ( ps -> A. y ph ) <-> ( ps -> A. x A. y ph ) )
4	2 3	bitri	|- ( A. x A. y ( ps -> ph ) <-> ( ps -> A. x A. y ph ) )