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Theorem mpanl1 661
Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)
Hypotheses
Ref Expression
mpanl1.1 φ
mpanl1.2 (((φ ψ) χ) → θ)
Assertion
Ref Expression
mpanl1 ((ψ χ) → θ)

Proof of Theorem mpanl1
StepHypRef Expression
1 mpanl1.1 . . 3 φ
21jctl 525 . 2 (ψ → (φ ψ))
3 mpanl1.2 . 2 (((φ ψ) χ) → θ)
42, 3sylan 457 1 ((ψ χ) → 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:  mpanl12  663
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