Theorem orbi1 742

Description: Theorem *4.37 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
orbi1	|- ( ( ph <-> ps ) -> ( ( ph \/ ch ) <-> ( ps \/ ch ) ) )

Proof of Theorem orbi1

Step	Hyp	Ref	Expression
1		id 22	. 2 |- ( ( ph <-> ps ) -> ( ph <-> ps ) )
2	1	orbi1d 739	1 |- ( ( ph <-> ps ) -> ( ( ph \/ ch ) <-> ( ps \/ ch ) ) )

Syntax hints:   -> wi 4   <-> wb 196   \/ wo 383

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

This theorem depends on definitions:  df-bi 197  df-or 385

This theorem is referenced by:  prmdvdsexp  15427  orbi1rVD  39083  sbc3orgVD  39086