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Theorem mp3an2 1265
Description: An inference based on modus ponens. (Contributed by NM, 21-Nov-1994.)
Hypotheses
Ref Expression
mp3an2.1 ψ
mp3an2.2 ((φ ψ χ) → θ)
Assertion
Ref Expression
mp3an2 ((φ χ) → θ)

Proof of Theorem mp3an2
StepHypRef Expression
1 mp3an2.1 . 2 ψ
2 mp3an2.2 . . 3 ((φ ψ χ) → θ)
323expa 1151 . 2 (((φ ψ) χ) → θ)
41, 3mpanl2 662 1 ((φ χ) → θ)
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:  mp3anl2  1272  oddtfin  4518  vfinncsp  4554
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