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Theorem mp3anl2 1457
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 414 . . 3 ((𝜑𝜓𝜒) → (𝜃𝜏))
41, 3mp3an2 1450 . 2 ((𝜑𝜒) → (𝜃𝜏))
54imp 408 1 (((𝜑𝜒) ∧ 𝜃) → 𝜏)
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:  mp3anr2  1460  preleq  9606  1dvds  16209  bcs2  30412  nmopub2tALT  31139  nmfnleub2  31156  nmophmi  31261  nmopcoadji  31331  atordi  31614  mdsymlem5  31637
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