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Theorem mp3anr1 1274
Description: An inference based on modus ponens. (Contributed by NM, 4-Nov-2006.)
Hypotheses
Ref Expression
mp3anr1.1 ψ
mp3anr1.2 ((φ (ψ χ θ)) → τ)
Assertion
Ref Expression
mp3anr1 ((φ (χ θ)) → τ)

Proof of Theorem mp3anr1
StepHypRef Expression
1 mp3anr1.1 . . 3 ψ
2 mp3anr1.2 . . . 4 ((φ (ψ χ θ)) → τ)
32ancoms 439 . . 3 (((ψ χ θ) φ) → τ)
41, 3mp3anl1 1271 . 2 (((χ θ) φ) → τ)
54ancoms 439 1 ((φ (χ 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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