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Theorem anmp 1716
Description: Modus ponens for ¬ axiom systems. (Contributed by Anthony Hart, 12-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
anmp.min 𝜑
anmp.maj 𝜑𝜓)
Assertion
Ref Expression
anmp 𝜓

Proof of Theorem anmp
StepHypRef Expression
1 anmp.min . 2 𝜑
2 anmp.maj . . 3 𝜑𝜓)
32imorri 429 . 2 (𝜑𝜓)
41, 3ax-mp 5 1 𝜓
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wo 382
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 197  df-or 384
This theorem is referenced by:  rbsyl  1721  rblem1  1722  rblem2  1723  rblem4  1725  rblem5  1726  rblem6  1727  rblem7  1728  re1axmp  1729  re2luk1  1730  re2luk2  1731  re2luk3  1732
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