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Theorem e000 28542
Description: A virtual deduction elimination rule. The non-virtual deduction form of e000 28542 is the virtual deduction form. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e000.1  |-  ph
e000.2  |-  ps
e000.3  |-  ch
e000.4  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
e000  |-  th

Proof of Theorem e000
StepHypRef Expression
1 e000.3 . 2  |-  ch
2 e000.1 . . 3  |-  ph
3 e000.2 . . 3  |-  ps
4 e000.4 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
52, 3, 4mp2 17 . 2  |-  ( ch 
->  th )
61, 5ax-mp 8 1  |-  th
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  a9e2ndeqVD  28685
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator