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Theorem mpdi 38
Description: A nested modus ponens deduction. (Contributed by NM, 16-Apr-2005.) (Proof shortened by O'Cat, 15-Jan-2008.)
Hypotheses
Ref Expression
mpdi.1 (ψχ)
mpdi.2 (φ → (ψ → (χθ)))
Assertion
Ref Expression
mpdi (φ → (ψθ))

Proof of Theorem mpdi
StepHypRef Expression
1 mpdi.1 . . 3 (ψχ)
21a1i 9 . 2 (φ → (ψχ))
3 mpdi.2 . 2 (φ → (ψ → (χθ)))
42, 3mpdd 36 1 (φ → (ψθ))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  mpii  39  pm2.43d  44  gencbval  2596  suctr  4124  tfrlem9  5876  lbzbi  8327  bj-inf2vnlem2  9431
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