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Theorem mp3anr2 1275
Description: An inference based on modus ponens. (Contributed by NM, 24-Nov-2006.)
Hypotheses
Ref Expression
mp3anr2.1 χ
mp3anr2.2 ((φ (ψ χ θ)) → τ)
Assertion
Ref Expression
mp3anr2 ((φ (ψ θ)) → τ)

Proof of Theorem mp3anr2
StepHypRef Expression
1 mp3anr2.1 . . 3 χ
2 mp3anr2.2 . . . 4 ((φ (ψ χ θ)) → τ)
32ancoms 439 . . 3 (((ψ χ θ) φ) → τ)
41, 3mp3anl2 1272 . 2 (((ψ θ) φ) → τ)
54ancoms 439 1 ((φ (ψ θ)) → τ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   w3a 934
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 177  df-an 360  df-3an 936
This theorem is referenced by: (None)
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