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Theorem mpd3an3 1233
 Description: An inference based on modus ponens. (Contributed by NM, 8-Nov-2007.)
Hypotheses
Ref Expression
mpd3an3.2 ((𝜑𝜓) → 𝜒)
mpd3an3.3 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
mpd3an3 ((𝜑𝜓) → 𝜃)

Proof of Theorem mpd3an3
StepHypRef Expression
1 mpd3an3.2 . 2 ((𝜑𝜓) → 𝜒)
2 mpd3an3.3 . . 3 ((𝜑𝜓𝜒) → 𝜃)
323expa 1104 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
41, 3mpdan 398 1 ((𝜑𝜓) → 𝜃)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∧ w3a 885 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101 This theorem depends on definitions:  df-bi 110  df-3an 887 This theorem is referenced by:  stoic2b  1319  elovmpt2  5701  oav  6034  omv  6035  oeiv  6036  f1oeng  6237  mulpipq2  6469  ltrnqg  6518  genipv  6607  subval  7203  fzrevral3  8969  fzoval  9005  subsq2  9359
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