Theorem pm4.39 768

Description: Theorem *4.39 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.39	|- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ( ph \/ ps ) <-> ( ch \/ th ) ) )

Proof of Theorem pm4.39

Step	Hyp	Ref	Expression
1		simpl 107	. 2 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ph <-> ch ) )
2		simpr 108	. 2 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ps <-> th ) )
3	1, 2	orbi12d 739	1 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ( ph \/ ps ) <-> ( ch \/ th ) ) )

Syntax hints:   -> wi 4   /\ wa 102   <-> wb 103   \/ wo 661

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662

This theorem depends on definitions:  df-bi 115

This theorem is referenced by: (None)