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Theorem mpanlr1 667
Description: An inference based on modus ponens. (Contributed by NM, 30-Dec-2004.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)
Hypotheses
Ref Expression
mpanlr1.1 ψ
mpanlr1.2 (((φ (ψ χ)) θ) → τ)
Assertion
Ref Expression
mpanlr1 (((φ χ) θ) → τ)

Proof of Theorem mpanlr1
StepHypRef Expression
1 mpanlr1.1 . . 3 ψ
21jctl 525 . 2 (χ → (ψ χ))
3 mpanlr1.2 . 2 (((φ (ψ χ)) θ) → τ)
42, 3sylanl2 632 1 (((φ χ) θ) → τ)
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: (None)
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