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Theorem 3anidm23 1297
Description: Inference from idempotent law for conjunction. (Contributed by NM, 1-Feb-2007.)
Hypothesis
Ref Expression
3anidm23.1 ((𝜑𝜓𝜓) → 𝜒)
Assertion
Ref Expression
3anidm23 ((𝜑𝜓) → 𝜒)

Proof of Theorem 3anidm23
StepHypRef Expression
1 3anidm23.1 . . 3 ((𝜑𝜓𝜓) → 𝜒)
213expa 1203 . 2 (((𝜑𝜓) ∧ 𝜓) → 𝜒)
32anabss3 585 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  efrirr  4353  subeq0  8181  halfaddsub  9151  avglt2  9156  efsub  11684  sinmul  11747  pythagtriplem4  12262  pythagtriplem16  12273  xmet0  13756
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