Theorem pm4.38 916

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 473	. 2 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ph <-> ch ) )
2		simpr 477	. 2 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ps <-> th ) )
3	1, 2	anbi12d 747	1 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ( ph /\ ps ) <-> ( ch /\ th ) ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ 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-an 386

This theorem is referenced by:  xpf1o  8122  isprm3  15396  csbingVD  39120  csbxpgVD  39130  csbunigVD  39134