Theorem pm3.44 705

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 700	. 2 |- ( ( ( ps \/ ch ) -> ph ) <-> ( ( ps -> ph ) /\ ( ch -> ph ) ) )
2	1	biimpri 132	1 |- ( ( ( ps -> ph ) /\ ( ch -> ph ) ) -> ( ( ps \/ ch ) -> ph ) )

Syntax hints:   -> wi 4   /\ wa 103   \/ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  jaoi  706  jao  745  pm2.6dc  852  pm4.83dc  941