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Theorem e31an 28842
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e31an.1  |-  (. ph ,. ps ,. ch  ->.  th ).
e31an.2  |-  (. ph  ->.  ta
).
e31an.3  |-  ( ( th  /\  ta )  ->  et )
Assertion
Ref Expression
e31an  |-  (. ph ,. ps ,. ch  ->.  et ).

Proof of Theorem e31an
StepHypRef Expression
1 e31an.1 . 2  |-  (. ph ,. ps ,. ch  ->.  th ).
2 e31an.2 . 2  |-  (. ph  ->.  ta
).
3 e31an.3 . . 3  |-  ( ( th  /\  ta )  ->  et )
43ex 423 . 2  |-  ( th 
->  ( ta  ->  et ) )
51, 2, 4e31 28840 1  |-  (. ph ,. ps ,. ch  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   (.wvd1 28636   (.wvd3 28655
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-vd1 28637  df-vd3 28658
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