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Theorem mp3anr3 1299
Description: An inference based on modus ponens. (Contributed by NM, 19-Oct-2007.)
Hypotheses
Ref Expression
mp3anr3.1 𝜃
mp3anr3.2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
mp3anr3 ((𝜑 ∧ (𝜓𝜒)) → 𝜏)

Proof of Theorem mp3anr3
StepHypRef Expression
1 mp3anr3.1 . . 3 𝜃
2 mp3anr3.2 . . . 4 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
32ancoms 266 . . 3 (((𝜓𝜒𝜃) ∧ 𝜑) → 𝜏)
41, 3mp3anl3 1296 . 2 (((𝜓𝜒) ∧ 𝜑) → 𝜏)
54ancoms 266 1 ((𝜑 ∧ (𝜓𝜒)) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by: (None)
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