Metamath Proof Explorer


Theorem e31

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e31.1
|- (. ph ,. ps ,. ch ->. th ).
e31.2
|- (. ph ->. ta ).
e31.3
|- ( th -> ( ta -> et ) )
Assertion e31
|- (. ph ,. ps ,. ch ->. et ).

Proof

Step Hyp Ref Expression
1 e31.1
 |-  (. ph ,. ps ,. ch ->. th ).
2 e31.2
 |-  (. ph ->. ta ).
3 e31.3
 |-  ( th -> ( ta -> et ) )
4 2 vd13
 |-  (. ph ,. ps ,. ch ->. ta ).
5 1 4 3 e33
 |-  (. ph ,. ps ,. ch ->. et ).