Theorem pm10.42 26927

Description: Theorem *10.42 in [WhiteheadRussell] p. 155. (Contributed by Andrew Salmon, 17-Jun-2011.)

Assertion

Ref	Expression
pm10.42	|- ( ( E. x ph \/ E. x ps ) <-> E. x ( ph \/ ps ) )

Proof of Theorem pm10.42

Step	Hyp	Ref	Expression
1		19.43 1604	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
2	1	bicomi 195	1 |- ( ( E. x ph \/ E. x ps ) <-> E. x ( ph \/ ps ) )

Syntax hints:   <-> wb 178   \/ wo 359   E.wex 1537

This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536

This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-ex 1538