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Theorem mp3anl1 1237
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 112 . . 3 ((𝜑𝜓𝜒) → (𝜃𝜏))
41, 3mp3an1 1230 . 2 ((𝜓𝜒) → (𝜃𝜏))
54imp 119 1 (((𝜓𝜒) ∧ 𝜃) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  mp3anr1  1240  archnqq  6572  facavg  9613  iddvds  10120
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