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Theorem mpand 656
Description: A deduction based on modus ponens. (Contributed by NM, 12-Dec-2004.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)
Hypotheses
Ref Expression
mpand.1 (φψ)
mpand.2 (φ → ((ψ χ) → θ))
Assertion
Ref Expression
mpand (φ → (χθ))

Proof of Theorem mpand
StepHypRef Expression
1 mpand.1 . 2 (φψ)
2 mpand.2 . . 3 (φ → ((ψ χ) → θ))
32ancomsd 440 . 2 (φ → ((χ ψ) → θ))
41, 3mpan2d 655 1 (φ → (χθ))
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:  mpani  657  mp2and  660  ecase2d  906  peano5  4409  sfinltfin  4535  vfinspss  4551  fvopab3ig  5387  ovig  5597  ncssfin  6151
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