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Theorem negel 32875
Description: An inference for negation elimination. (Contributed by Giovanni Mascellani, 24-May-2019.)
Hypotheses
Ref Expression
negel.1 (𝜓𝜒)
negel.2 (𝜑 → ¬ 𝜒)
Assertion
Ref Expression
negel ((𝜑𝜓) → ⊥)

Proof of Theorem negel
StepHypRef Expression
1 negel.1 . . 3 (𝜓𝜒)
21adantl 480 . 2 ((𝜑𝜓) → 𝜒)
3 negel.2 . . 3 (𝜑 → ¬ 𝜒)
43adantr 479 . 2 ((𝜑𝜓) → ¬ 𝜒)
52, 4pm2.21fal 1495 1 ((𝜑𝜓) → ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 382  wfal 1479
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 195  df-an 384
This theorem is referenced by: (None)
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