Metamath Proof Explorer


Theorem e221

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

Ref Expression
Hypotheses e221.1
|- (. ph ,. ps ->. ch ).
e221.2
|- (. ph ,. ps ->. th ).
e221.3
|- (. ph ->. ta ).
e221.4
|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion e221
|- (. ph ,. ps ->. et ).

Proof

Step Hyp Ref Expression
1 e221.1
 |-  (. ph ,. ps ->. ch ).
2 e221.2
 |-  (. ph ,. ps ->. th ).
3 e221.3
 |-  (. ph ->. ta ).
4 e221.4
 |-  ( ch -> ( th -> ( ta -> et ) ) )
5 3 vd12
 |-  (. ph ,. ps ->. ta ).
6 1 2 5 4 e222
 |-  (. ph ,. ps ->. et ).