Metamath Proof Explorer


Theorem e122

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

Ref Expression
Hypotheses e122.1
|- (. ph ->. ps ).
e122.2
|- (. ph ,. ch ->. th ).
e122.3
|- (. ph ,. ch ->. ta ).
e122.4
|- ( ps -> ( th -> ( ta -> et ) ) )
Assertion e122
|- (. ph ,. ch ->. et ).

Proof

Step Hyp Ref Expression
1 e122.1
 |-  (. ph ->. ps ).
2 e122.2
 |-  (. ph ,. ch ->. th ).
3 e122.3
 |-  (. ph ,. ch ->. ta ).
4 e122.4
 |-  ( ps -> ( th -> ( ta -> et ) ) )
5 1 vd12
 |-  (. ph ,. ch ->. ps ).
6 5 2 3 4 e222
 |-  (. ph ,. ch ->. et ).