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Theorem 3anidm12 1420
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 1123 . 2 (𝜑 → ((𝜑𝜓) → 𝜒))
32anabsi5 668 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  w3a 1088
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 206  df-an 398  df-3an 1090
This theorem is referenced by:  3anidm13  1421  syl2an3an  1423  dedth3v  4590  fovcl  7532  nncan  11485  divid  11897  sqdivid  14083  subsq  14170  o1lo1  15477  retancl  16081  tanneg  16087  gcd0id  16456  coprm  16644  ablonncan  29787  kbpj  31187  xdivid  32072  xrsmulgzz  32157  f1resrcmplf1dlem  34027  expgrowthi  43025  dvconstbi  43026  3ornot23  43203  3anidm12p2  43501  sinhpcosh  47687  reseccl  47700  recsccl  47701  recotcl  47702  onetansqsecsq  47708
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