Theorem 19.28vv

Description: Theorem *11.47 in WhiteheadRussell p. 164. Theorem 19.28 of Margaris p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	19.28vv	|- ( A. x A. y ( ps /\ ph ) <-> ( ps /\ A. x A. y ph ) )

Proof

Step	Hyp	Ref	Expression
1		19.28v	|- ( A. y ( ps /\ ph ) <-> ( ps /\ A. y ph ) )
2	1	albii	|- ( A. x A. y ( ps /\ ph ) <-> A. x ( ps /\ A. y ph ) )
3		19.28v	|- ( 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 ) )