Theorem 19.37vv

Description: Theorem *11.46 in WhiteheadRussell p. 164. Theorem 19.37 of Margaris p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	19.37vv	|- ( E. x E. y ( ps -> ph ) <-> ( ps -> E. x E. y ph ) )

Proof

Step	Hyp	Ref	Expression
1		19.37v	|- ( E. y ( ps -> ph ) <-> ( ps -> E. y ph ) )
2	1	exbii	|- ( E. x E. y ( ps -> ph ) <-> E. x ( ps -> E. y ph ) )
3		19.37v	|- ( E. x ( ps -> E. y ph ) <-> ( ps -> E. x E. y ph ) )
4	2 3	bitri	|- ( E. x E. y ( ps -> ph ) <-> ( ps -> E. x E. y ph ) )