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Theorem mpan2d 655
Description: A deduction based on modus ponens. (Contributed by NM, 12-Dec-2004.)
Hypotheses
Ref Expression
mpan2d.1 (φχ)
mpan2d.2 (φ → ((ψ χ) → θ))
Assertion
Ref Expression
mpan2d (φ → (ψθ))

Proof of Theorem mpan2d
StepHypRef Expression
1 mpan2d.1 . 2 (φχ)
2 mpan2d.2 . . 3 (φ → ((ψ χ) → θ))
32exp3a 425 . 2 (φ → (ψ → (χθ)))
41, 3mpid 37 1 (φ → (ψθ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  mpand  656  mpan2i  658  ltfintri  4466  leconnnc  6218  nclenn  6249  ncslesuc  6267  nchoicelem4  6292
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