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Theorem 3anidm12 1203
Description: Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)
Hypothesis
Ref Expression
3anidm12.1 ((𝜑𝜑𝜓) → 𝜒)
Assertion
Ref Expression
3anidm12 ((𝜑𝜓) → 𝜒)

Proof of Theorem 3anidm12
StepHypRef Expression
1 3anidm12.1 . . 3 ((𝜑𝜑𝜓) → 𝜒)
213expib 1118 . 2 (𝜑 → ((𝜑𝜓) → 𝜒))
32anabsi5 521 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  w3a 896
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 898
This theorem is referenced by:  3anidm13  1204  prarloclemarch2  6575  nq02m  6621  recexprlem1ssl  6789  recexprlem1ssu  6790  nncan  7303  dividap  7752  modqid0  9300  subsq  9525
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