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Theorem mpnanrd 33308
Description: Eliminate the right side of a negated conjunction in an implication. (Contributed by ML, 17-Oct-2020.)
Hypotheses
Ref Expression
mpnanrd.1 (𝜑𝜓)
mpnanrd.2 (𝜑 → ¬ (𝜓𝜒))
Assertion
Ref Expression
mpnanrd (𝜑 → ¬ 𝜒)

Proof of Theorem mpnanrd
StepHypRef Expression
1 mpnanrd.1 . 2 (𝜑𝜓)
2 mpnanrd.2 . . 3 (𝜑 → ¬ (𝜓𝜒))
3 imnan 437 . . 3 ((𝜓 → ¬ 𝜒) ↔ ¬ (𝜓𝜒))
42, 3sylibr 224 . 2 (𝜑 → (𝜓 → ¬ 𝜒))
51, 4mpd 15 1 (𝜑 → ¬ 𝜒)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 383
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-an 385
This theorem is referenced by:  onsucuni3  33345
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