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Theorem mpanr2 665
Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)
Hypotheses
Ref Expression
mpanr2.1 χ
mpanr2.2 ((φ (ψ χ)) → θ)
Assertion
Ref Expression
mpanr2 ((φ ψ) → θ)

Proof of Theorem mpanr2
StepHypRef Expression
1 mpanr2.1 . . 3 χ
21jctr 526 . 2 (ψ → (ψ χ))
3 mpanr2.2 . 2 ((φ (ψ χ)) → θ)
42, 3sylan2 460 1 ((φ ψ) → θ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
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
This theorem is referenced by:  eladdci  4399
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