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Theorem mp3an12 1267
 Description: An inference based on modus ponens. (Contributed by NM, 13-Jul-2005.)
Hypotheses
Ref Expression
mp3an12.1 φ
mp3an12.2 ψ
mp3an12.3 ((φ ψ χ) → θ)
Assertion
Ref Expression
mp3an12 (χθ)

Proof of Theorem mp3an12
StepHypRef Expression
1 mp3an12.2 . 2 ψ
2 mp3an12.1 . . 3 φ
3 mp3an12.3 . . 3 ((φ ψ χ) → θ)
42, 3mp3an1 1264 . 2 ((ψ χ) → θ)
51, 4mpan 651 1 (χθ)
 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:  ceqsralv  2886  opkelopkabg  4245  otkelins2kg  4253  otkelins3kg  4254  opkelcokg  4261  vfin1cltv  4547  vfinspss  4551  fvfullfunlem3  5863  fvfullfun  5864  clos1nrel  5886  cenc  6181  nclec  6195  nc0le1  6216  nclenc  6222
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