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Theorem 3anidm23 1203
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 1113 . 2 (((𝜑𝜓) ∧ 𝜓) → 𝜒)
32anabss3 527 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  w3a 894
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 896
This theorem is referenced by:  efrirr  4115  subeq0  7270  halfaddsub  8186  avglt2  8191
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