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Theorem mp3anr1 1240
Description: An inference based on modus ponens. (Contributed by NM, 4-Nov-2006.)
Hypotheses
Ref Expression
mp3anr1.1 𝜓
mp3anr1.2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
mp3anr1 ((𝜑 ∧ (𝜒𝜃)) → 𝜏)

Proof of Theorem mp3anr1
StepHypRef Expression
1 mp3anr1.1 . . 3 𝜓
2 mp3anr1.2 . . . 4 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
32ancoms 259 . . 3 (((𝜓𝜒𝜃) ∧ 𝜑) → 𝜏)
41, 3mp3anl1 1237 . 2 (((𝜒𝜃) ∧ 𝜑) → 𝜏)
54ancoms 259 1 ((𝜑 ∧ (𝜒𝜃)) → 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: (None)
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