Metamath Proof Explorer


Theorem e30an

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

Ref Expression
Hypotheses e30an.1
|- (. ph ,. ps ,. ch ->. th ).
e30an.2
|- ta
e30an.3
|- ( ( th /\ ta ) -> et )
Assertion e30an
|- (. ph ,. ps ,. ch ->. et ).

Proof

Step Hyp Ref Expression
1 e30an.1
 |-  (. ph ,. ps ,. ch ->. th ).
2 e30an.2
 |-  ta
3 e30an.3
 |-  ( ( th /\ ta ) -> et )
4 3 ex
 |-  ( th -> ( ta -> et ) )
5 1 2 4 e30
 |-  (. ph ,. ps ,. ch ->. et ).