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Theorem mpanr12 666
Description: An inference based on modus ponens. (Contributed by NM, 24-Jul-2009.)
Hypotheses
Ref Expression
mpanr12.1 ψ
mpanr12.2 χ
mpanr12.3 ((φ (ψ χ)) → θ)
Assertion
Ref Expression
mpanr12 (φθ)

Proof of Theorem mpanr12
StepHypRef Expression
1 mpanr12.2 . 2 χ
2 mpanr12.1 . . 3 ψ
3 mpanr12.3 . . 3 ((φ (ψ χ)) → θ)
42, 3mpanr1 664 . 2 ((φ χ) → θ)
51, 4mpan2 652 1 (φθ)
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:  sbthlem1  6203
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