Metamath Proof Explorer


Theorem e23an

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e23an.1
|- (. ph ,. ps ->. ch ).
e23an.2
|- (. ph ,. ps ,. th ->. ta ).
e23an.3
|- ( ( ch /\ ta ) -> et )
Assertion e23an
|- (. ph ,. ps ,. th ->. et ).

Proof

Step Hyp Ref Expression
1 e23an.1
 |-  (. ph ,. ps ->. ch ).
2 e23an.2
 |-  (. ph ,. ps ,. th ->. ta ).
3 e23an.3
 |-  ( ( ch /\ ta ) -> et )
4 3 ex
 |-  ( ch -> ( ta -> et ) )
5 1 2 4 e23
 |-  (. ph ,. ps ,. th ->. et ).