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Theorem mp3anl2 1453
 Description: An inference based on modus ponens. (Contributed by NM, 24-Feb-2005.)
Hypotheses
Ref Expression
mp3anl2.1 𝜓
mp3anl2.2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
mp3anl2 (((𝜑𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem mp3anl2
StepHypRef Expression
1 mp3anl2.1 . . 3 𝜓
2 mp3anl2.2 . . . 4 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
32ex 416 . . 3 ((𝜑𝜓𝜒) → (𝜃𝜏))
41, 3mp3an2 1446 . 2 ((𝜑𝜒) → (𝜃𝜏))
54imp 410 1 (((𝜑𝜒) ∧ 𝜃) → 𝜏)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1084 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 210  df-an 400  df-3an 1086 This theorem is referenced by:  mp3anr2  1456  preleq  9065  ccat2s1fstOLD  13994  1dvds  15618  bcs2  28972  nmopub2tALT  29699  nmfnleub2  29716  nmophmi  29821  nmopcoadji  29891  atordi  30174  mdsymlem5  30197
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