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Axiom ax-in2 587
Description: 'Not' elimination. One of the axioms of propositional logic. (Contributed by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
ax-in2 𝜑 → (𝜑𝜓))

Detailed syntax breakdown of Axiom ax-in2
StepHypRef Expression
1 wph . . 3 wff 𝜑
21wn 3 . 2 wff ¬ 𝜑
3 wps . . 3 wff 𝜓
41, 3wi 4 . 2 wff (𝜑𝜓)
52, 4wi 4 1 wff 𝜑 → (𝜑𝜓))
Colors of variables: wff set class
This axiom is referenced by:  pm2.21  589  con2d  596  imorr  693  dcim  809  condcOLD  822  pm5.14dc  879  pm5.54dc  886  mon  2004  difin  3281  indifdir  3300  sosng  4580  iotanul  5071
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