Theorem 19.21vv 38575

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 1868. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

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

Distinct variable groups:   ps, x   ps, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem 19.21vv

Step	Hyp	Ref	Expression
1		19.21v 1868	. . 3 |- ( A. y ( ps -> ph ) <-> ( ps -> A. y ph ) )
2	1	albii 1747	. 2 |- ( A. x A. y ( ps -> ph ) <-> A. x ( ps -> A. y ph ) )
3		19.21v 1868	. 2 |- ( A. x ( ps -> A. y ph ) <-> ( ps -> A. x A. y ph ) )
4	2, 3	bitri 264	1 |- ( A. x A. y ( ps -> ph ) <-> ( ps -> A. x A. y ph ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by: (None)