Theorem pm4.38 594

Description: Theorem *4.38 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.38	|- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ( ph /\ ps ) <-> ( ch /\ th ) ) )

Proof of Theorem pm4.38

Step	Hyp	Ref	Expression
1		simpl 108	. 2 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ph <-> ch ) )
2		simpr 109	. 2 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ps <-> th ) )
3	1, 2	anbi12d 464	1 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ( ph /\ ps ) <-> ( ch /\ th ) ) )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  xpf1o  6738  isprm3  11799