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Theorem mpdi 42
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 40 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  43  pm2.43d  48  gencbval  2619  sbcimdv  2851  suctr  4186  tfrlem9  5966  lbzbi  8648  flqeqceilz  9268  ndvdsadd  10243  bj-inf2vnlem2  10483
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