Theorem pm3.44 667

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 663	. 2 |- ( ( ( ps \/ ch ) -> ph ) <-> ( ( ps -> ph ) /\ ( ch -> ph ) ) )
2	1	biimpri 131	1 |- ( ( ( ps -> ph ) /\ ( ch -> ph ) ) -> ( ( ps \/ ch ) -> ph ) )

Syntax hints:   -> wi 4   /\ wa 102   \/ wo 661

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  jaoi  668  jao  704  pm2.6dc  792  pm4.83dc  892