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Theorem efald2 31757
Description: A proof by contradiction. (Contributed by Giovanni Mascellani, 15-Sep-2017.)
Hypothesis
Ref Expression
efald2.1  |-  ( -. 
ph  -> F.  )
Assertion
Ref Expression
efald2  |-  ph

Proof of Theorem efald2
StepHypRef Expression
1 efald2.1 . . . 4  |-  ( -. 
ph  -> F.  )
21adantl 464 . . 3  |-  ( ( T.  /\  -.  ph )  -> F.  )
32efald 1427 . 2  |-  ( T. 
->  ph )
43trud 1414 1  |-  ph
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   T. wtru 1406   F. wfal 1410
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-fal 1411
This theorem is referenced by:  mpt2bi123f  31853  mptbi12f  31857  ac6s6  31862
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