Theorem pm10.42 26970

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 1592	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
2	1	bicomi 193	1 |- ( ( E. x ph \/ E. x ps ) <-> E. x ( ph \/ ps ) )

Syntax hints:   <-> wb 176   \/ wo 357   E.wex 1528

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-ex 1529