Theorem pm11.53

Description: Theorem *11.53 in WhiteheadRussell p. 164. See pm11.53v for a version requiring fewer axioms. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	pm11.53	|- ( A. x A. y ( ph -> ps ) <-> ( E. x ph -> A. y ps ) )

Proof

Step	Hyp	Ref	Expression
1		19.21v	|- ( A. y ( ph -> ps ) <-> ( ph -> A. y ps ) )
2	1	albii	|- ( A. x A. y ( ph -> ps ) <-> A. x ( ph -> A. y ps ) )
3		nfv	|- F/ x ps
4	3	nfal	|- F/ x A. y ps
5	4	19.23	|- ( A. x ( ph -> A. y ps ) <-> ( E. x ph -> A. y ps ) )
6	2 5	bitri	|- ( A. x A. y ( ph -> ps ) <-> ( E. x ph -> A. y ps ) )