Theorem pm11.12 38574

Description: Theorem *11.12 in [WhiteheadRussell] p. 159. (Contributed by Andrew Salmon, 17-Jun-2011.)

Assertion

Ref	Expression
pm11.12	|- ( A. x A. y ( ph \/ ps ) -> ( ph \/ A. x A. y ps ) )

Distinct variable groups:   ph, x   ph, y

Allowed substitution hints:   ps( x, y)

Proof of Theorem pm11.12

Step	Hyp	Ref	Expression
1		pm10.12 38557	. . 3 |- ( A. y ( ph \/ ps ) -> ( ph \/ A. y ps ) )
2	1	alimi 1739	. 2 |- ( A. x A. y ( ph \/ ps ) -> A. x ( ph \/ A. y ps ) )
3		pm10.12 38557	. 2 |- ( A. x ( ph \/ A. y ps ) -> ( ph \/ A. x A. y ps ) )
4	2, 3	syl 17	1 |- ( A. x A. y ( ph \/ ps ) -> ( ph \/ A. x A. y ps ) )

Syntax hints:   -> wi 4   \/ wo 383   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-or 385  df-ex 1705

This theorem is referenced by: (None)