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Metamath Proof Explorer

Theorem pm3.44

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

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

Proof

Step Hyp Ref Expression
1 id 
 |-  ( ( ps -> ph ) -> ( ps -> ph ) )
2 id 
 |-  ( ( ch -> ph ) -> ( ch -> ph ) )
3 1 2 jaao 
 |-  ( ( ( ps -> ph ) /\ ( ch -> ph ) ) -> ( ( ps \/ ch ) -> ph ) )