Theorem pm10.542 38567

Description: Theorem *10.542 in [WhiteheadRussell] p. 156. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
pm10.542	|- ( A. x ( ph -> ( ch -> ps ) ) <-> ( ch -> A. x ( ph -> ps ) ) )

Distinct variable group:   ch, x

Allowed substitution hints:   ph( x)   ps( x)

Proof of Theorem pm10.542

Step	Hyp	Ref	Expression
1		bi2.04 376	. . 3 |- ( ( ph -> ( ch -> ps ) ) <-> ( ch -> ( ph -> ps ) ) )
2	1	albii 1747	. 2 |- ( A. x ( ph -> ( ch -> ps ) ) <-> A. x ( ch -> ( ph -> ps ) ) )
3		19.21v 1868	. 2 |- ( A. x ( ch -> ( ph -> ps ) ) <-> ( ch -> A. x ( ph -> ps ) ) )
4	2, 3	bitri 264	1 |- ( A. x ( ph -> ( ch -> ps ) ) <-> ( ch -> A. x ( ph -> ps ) ) )

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)