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Theorem bj-imn3ani 32697
 Description: Duplication of bnj1224 30998. Three-fold version of imnani 438. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Revised by BJ, 22-Oct-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-imn3ani.1 ¬ (𝜑𝜓𝜒)
Assertion
Ref Expression
bj-imn3ani ((𝜑𝜓) → ¬ 𝜒)

Proof of Theorem bj-imn3ani
StepHypRef Expression
1 bj-imn3ani.1 . . 3 ¬ (𝜑𝜓𝜒)
2 df-3an 1056 . . 3 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ 𝜒))
31, 2mtbi 311 . 2 ¬ ((𝜑𝜓) ∧ 𝜒)
43imnani 438 1 ((𝜑𝜓) → ¬ 𝜒)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 383   ∧ w3a 1054 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  df-3an 1056 This theorem is referenced by:  bj-inftyexpidisj  33227
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