Metamath Proof Explorer


Theorem e202

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

Ref Expression
Hypotheses e202.1
|- (. ph ,. ps ->. ch ).
e202.2
|- th
e202.3
|- (. ph ,. ps ->. ta ).
e202.4
|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion e202
|- (. ph ,. ps ->. et ).

Proof

Step Hyp Ref Expression
1 e202.1
 |-  (. ph ,. ps ->. ch ).
2 e202.2
 |-  th
3 e202.3
 |-  (. ph ,. ps ->. ta ).
4 e202.4
 |-  ( ch -> ( th -> ( ta -> et ) ) )
5 2 vd02
 |-  (. ph ,. ps ->. th ).
6 1 5 3 4 e222
 |-  (. ph ,. ps ->. et ).