Theorem pm10.42 27435

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 1612	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
2	1	bicomi 194	1 |- ( ( E. x ph \/ E. x ps ) <-> E. x ( ph \/ ps ) )

Syntax hints:   <-> wb 177   \/ wo 358   E.wex 1547

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563

This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-ex 1548