Theorem pm5.3 458

Description: Theorem *5.3 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Assertion

Ref	Expression
pm5.3	|- ( ( ( ph /\ ps ) -> ch ) <-> ( ( ph /\ ps ) -> ( ph /\ ch ) ) )

Proof of Theorem pm5.3

Step	Hyp	Ref	Expression
1		impexp 259	. 2 |- ( ( ( ph /\ ps ) -> ch ) <-> ( ph -> ( ps -> ch ) ) )
2		imdistan 432	. 2 |- ( ( ph -> ( ps -> ch ) ) <-> ( ( ph /\ ps ) -> ( ph /\ ch ) ) )
3	1, 2	bitri 182	1 |- ( ( ( ph /\ ps ) -> ch ) <-> ( ( ph /\ ps ) -> ( ph /\ ch ) ) )

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

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

This theorem depends on definitions:  df-bi 115

This theorem is referenced by: (None)