Metamath Proof Explorer


Theorem ee22an

Description: e22an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee22an.1
|- ( ph -> ( ps -> ch ) )
ee22an.2
|- ( ph -> ( ps -> th ) )
ee22an.3
|- ( ( ch /\ th ) -> ta )
Assertion ee22an
|- ( ph -> ( ps -> ta ) )

Proof

Step Hyp Ref Expression
1 ee22an.1
 |-  ( ph -> ( ps -> ch ) )
2 ee22an.2
 |-  ( ph -> ( ps -> th ) )
3 ee22an.3
 |-  ( ( ch /\ th ) -> ta )
4 3 ex
 |-  ( ch -> ( th -> ta ) )
5 1 2 4 syl6c
 |-  ( ph -> ( ps -> ta ) )