Theorem pm3.44 635

Description: Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 3-Oct-2013.)

Assertion

Ref	Expression
pm3.44	|- ( ( ( ps -> ph ) /\ ( ch -> ph ) ) -> ( ( ps \/ ch ) -> ph ) )

Proof of Theorem pm3.44

Step	Hyp	Ref	Expression
1		jaob 631	. 2 |- ( ( ( ps \/ ch ) -> ph ) <-> ( ( ps -> ph ) /\ ( ch -> ph ) ) )
2	1	biimpri 124	1 |- ( ( ( ps -> ph ) /\ ( ch -> ph ) ) -> ( ( ps \/ ch ) -> ph ) )

Syntax hints:   -> wi 4   /\ wa 97   \/ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  jaoi  636  jao  672  pm2.6dc  759  pm4.83dc  858