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Theorem mp3an13 1268
Description: An inference based on modus ponens. (Contributed by NM, 14-Jul-2005.)
Hypotheses
Ref Expression
mp3an13.1 φ
mp3an13.2 χ
mp3an13.3 ((φ ψ χ) → θ)
Assertion
Ref Expression
mp3an13 (ψθ)

Proof of Theorem mp3an13
StepHypRef Expression
1 mp3an13.1 . 2 φ
2 mp3an13.2 . . 3 χ
3 mp3an13.3 . . 3 ((φ ψ χ) → θ)
42, 3mp3an3 1266 . 2 ((φ ψ) → θ)
51, 4mpan 651 1 (ψθ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   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:  sfinltfin  4535  nmembers1lem2  6269
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