Metamath Proof Explorer


Theorem e12

Description: A virtual deduction elimination rule (see sylsyld ). (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e12.1
|- (. ph ->. ps ).
e12.2
|- (. ph ,. ch ->. th ).
e12.3
|- ( ps -> ( th -> ta ) )
Assertion e12
|- (. ph ,. ch ->. ta ).

Proof

Step Hyp Ref Expression
1 e12.1
 |-  (. ph ->. ps ).
2 e12.2
 |-  (. ph ,. ch ->. th ).
3 e12.3
 |-  ( ps -> ( th -> ta ) )
4 1 vd12
 |-  (. ph ,. ch ->. ps ).
5 4 2 3 e22
 |-  (. ph ,. ch ->. ta ).