Theorem pm10.12 38557

Description: Theorem *10.12 in [WhiteheadRussell] p. 146. In *10, this is treated as an axiom, and the proofs in *10 are based on this theorem. (Contributed by Andrew Salmon, 17-Jun-2011.)

Assertion

Ref	Expression
pm10.12	|- ( A. x ( ph \/ ps ) -> ( ph \/ A. x ps ) )

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem pm10.12

Step	Hyp	Ref	Expression
1		19.32v 1869	. 2 |- ( A. x ( ph \/ ps ) <-> ( ph \/ A. x ps ) )
2	1	biimpi 206	1 |- ( A. x ( ph \/ ps ) -> ( ph \/ A. x 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:  pm11.12  38574