Metamath Proof Explorer


Theorem e100

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

Ref Expression
Hypotheses e100.1
|- (. ph ->. ps ).
e100.2
|- ch
e100.3
|- th
e100.4
|- ( ps -> ( ch -> ( th -> ta ) ) )
Assertion e100
|- (. ph ->. ta ).

Proof

Step Hyp Ref Expression
1 e100.1
 |-  (. ph ->. ps ).
2 e100.2
 |-  ch
3 e100.3
 |-  th
4 e100.4
 |-  ( ps -> ( ch -> ( th -> ta ) ) )
5 2 vd01
 |-  (. ph ->. ch ).
6 3 vd01
 |-  (. ph ->. th ).
7 1 5 6 4 e111
 |-  (. ph ->. ta ).