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Theorem mp3anr2 1419
Description: An inference based on modus ponens. (Contributed by NM, 24-Nov-2006.)
Hypotheses
Ref Expression
mp3anr2.1 𝜒
mp3anr2.2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
mp3anr2 ((𝜑 ∧ (𝜓𝜃)) → 𝜏)

Proof of Theorem mp3anr2
StepHypRef Expression
1 mp3anr2.1 . . 3 𝜒
2 mp3anr2.2 . . . 4 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
32ancoms 469 . . 3 (((𝜓𝜒𝜃) ∧ 𝜑) → 𝜏)
41, 3mp3anl2 1416 . 2 (((𝜓𝜃) ∧ 𝜑) → 𝜏)
54ancoms 469 1 ((𝜑 ∧ (𝜓𝜃)) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
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 386  df-3an 1038
This theorem is referenced by:  mulgp1  17506  vcz  27300  nvmdi  27373
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