Metamath Proof Explorer


Theorem e02an

Description: Conjunction form of e02 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e02an.1
|- ph
e02an.2
|- (. ps ,. ch ->. th ).
e02an.3
|- ( ( ph /\ th ) -> ta )
Assertion e02an
|- (. ps ,. ch ->. ta ).

Proof

Step Hyp Ref Expression
1 e02an.1
 |-  ph
2 e02an.2
 |-  (. ps ,. ch ->. th ).
3 e02an.3
 |-  ( ( ph /\ th ) -> ta )
4 3 ex
 |-  ( ph -> ( th -> ta ) )
5 1 2 4 e02
 |-  (. ps ,. ch ->. ta ).