Theorem 19.36vv

Description: Theorem *11.43 in WhiteheadRussell p. 163. Theorem 19.36 of Margaris p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 25-May-2011)

	Ref	Expression
Assertion	19.36vv	|- ( E. x E. y ( ph -> ps ) <-> ( A. x A. y ph -> ps ) )

Proof

Step	Hyp	Ref	Expression
1		19.36v	|- ( E. y ( ph -> ps ) <-> ( A. y ph -> ps ) )
2	1	exbii	|- ( E. x E. y ( ph -> ps ) <-> E. x ( A. y ph -> ps ) )
3		19.36v	|- ( E. x ( A. y ph -> ps ) <-> ( A. x A. y ph -> ps ) )
4	2 3	bitri	|- ( E. x E. y ( ph -> ps ) <-> ( A. x A. y ph -> ps ) )