Metamath Proof Explorer


Theorem el021old

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses el021old.1
|- ph
el021old.2
|- (. (. ps ,. ch ). ->. th ).
el021old.3
|- ( ( ph /\ th ) -> ta )
Assertion el021old
|- (. (. ps ,. ch ). ->. ta ).

Proof

Step Hyp Ref Expression
1 el021old.1
 |-  ph
2 el021old.2
 |-  (. (. ps ,. ch ). ->. th ).
3 el021old.3
 |-  ( ( ph /\ th ) -> ta )
4 2 dfvd2ani
 |-  ( ( ps /\ ch ) -> th )
5 1 4 3 sylancr
 |-  ( ( ps /\ ch ) -> ta )
6 5 dfvd2anir
 |-  (. (. ps ,. ch ). ->. ta ).