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Theorem mp3anl1 1567
Description: An inference based on modus ponens. (Contributed by NM, 24-Feb-2005.)
Hypotheses
Ref Expression
mp3anl1.1 𝜑
mp3anl1.2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
mp3anl1 (((𝜓𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem mp3anl1
StepHypRef Expression
1 mp3anl1.1 . . 3 𝜑
2 mp3anl1.2 . . . 4 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
32ex 449 . . 3 ((𝜑𝜓𝜒) → (𝜃𝜏))
41, 3mp3an1 1560 . 2 ((𝜓𝜒) → (𝜃𝜏))
54imp 444 1 (((𝜓𝜒) ∧ 𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1072
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 197  df-an 385  df-3an 1074
This theorem is referenced by:  mp3anr1  1570  facavg  13282  iddvds  15197  isprm7  15622  blometi  27967  mdslmd3i  29500  atcvat2i  29555  chirredlem3  29560  mdsymlem1  29571
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