Metamath Proof Explorer


Theorem e010

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

Ref Expression
Hypotheses e010.1
|- ph
e010.2
|- (. ps ->. ch ).
e010.3
|- th
e010.4
|- ( ph -> ( ch -> ( th -> ta ) ) )
Assertion e010
|- (. ps ->. ta ).

Proof

Step Hyp Ref Expression
1 e010.1
 |-  ph
2 e010.2
 |-  (. ps ->. ch ).
3 e010.3
 |-  th
4 e010.4
 |-  ( ph -> ( ch -> ( th -> ta ) ) )
5 1 vd01
 |-  (. ps ->. ph ).
6 3 vd01
 |-  (. ps ->. th ).
7 5 2 6 4 e111
 |-  (. ps ->. ta ).