This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pm2.74

Description: Theorem *2.74 of WhiteheadRussell p. 108. (Contributed by NM, 3-Jan-2005) (Proof shortened by Andrew Salmon, 7-May-2011)

Ref Expression
Assertion pm2.74 
|- ( ( ps -> ph ) -> ( ( ( ph \/ ps ) \/ ch ) -> ( ph \/ ch ) ) )

Proof

Step Hyp Ref Expression
1 orel2 
 |-  ( -. ps -> ( ( ph \/ ps ) -> ph ) )
2 ax-1 
 |-  ( ph -> ( ( ph \/ ps ) -> ph ) )
3 1 2 ja 
 |-  ( ( ps -> ph ) -> ( ( ph \/ ps ) -> ph ) )
4 3 orim1d 
 |-  ( ( ps -> ph ) -> ( ( ( ph \/ ps ) \/ ch ) -> ( ph \/ ch ) ) )