Metamath Proof Explorer


Theorem e10an

Description: Conjunction form of e10 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e10an.1
|- (. ph ->. ps ).
e10an.2
|- ch
e10an.3
|- ( ( ps /\ ch ) -> th )
Assertion e10an
|- (. ph ->. th ).

Proof

Step Hyp Ref Expression
1 e10an.1
 |-  (. ph ->. ps ).
2 e10an.2
 |-  ch
3 e10an.3
 |-  ( ( ps /\ ch ) -> th )
4 3 ex
 |-  ( ps -> ( ch -> th ) )
5 1 2 4 e10
 |-  (. ph ->. th ).