Theorem pm4.39 915

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 473	. 2 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ph <-> ch ) )
2		simpr 477	. 2 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ps <-> th ) )
3	1, 2	orbi12d 746	1 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ( ph \/ ps ) <-> ( ch \/ th ) ) )

Syntax hints:   -> wi 4   <-> wb 196   \/ wo 383   /\ wa 384

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  df-an 386

This theorem is referenced by:  3orbi123VD  39085