Metamath Proof Explorer


Theorem e21

Description: A virtual deduction elimination rule (see syl6ci ). (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e21.1
|- (. ph ,. ps ->. ch ).
e21.2
|- (. ph ->. th ).
e21.3
|- ( ch -> ( th -> ta ) )
Assertion e21
|- (. ph ,. ps ->. ta ).

Proof

Step Hyp Ref Expression
1 e21.1
 |-  (. ph ,. ps ->. ch ).
2 e21.2
 |-  (. ph ->. th ).
3 e21.3
 |-  ( ch -> ( th -> ta ) )
4 2 vd12
 |-  (. ph ,. ps ->. th ).
5 1 4 3 e22
 |-  (. ph ,. ps ->. ta ).