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Theorem anmp 1745
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 853 . 2 (𝜑𝜓)
41, 3ax-mp 5 1 𝜓
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wo 845
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 206  df-or 846
This theorem is referenced by:  rbsyl  1750  rblem1  1751  rblem2  1752  rblem4  1754  rblem5  1755  rblem6  1756  rblem7  1757  re1axmp  1758  re2luk1  1759  re2luk2  1760  re2luk3  1761
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