Metamath Proof Explorer


Theorem e03an

Description: Conjunction form of e03 . (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e03an.1
|- ph
e03an.2
|- (. ps ,. ch ,. th ->. ta ).
e03an.3
|- ( ( ph /\ ta ) -> et )
Assertion e03an
|- (. ps ,. ch ,. th ->. et ).

Proof

Step Hyp Ref Expression
1 e03an.1
 |-  ph
2 e03an.2
 |-  (. ps ,. ch ,. th ->. ta ).
3 e03an.3
 |-  ( ( ph /\ ta ) -> et )
4 3 ex
 |-  ( ph -> ( ta -> et ) )
5 1 2 4 e03
 |-  (. ps ,. ch ,. th ->. et ).