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Theorem mpdi 43
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 41 1 (𝜑 → (𝜓𝜃))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  mpii  44  pm2.43d  50  gencbval  2778  sbcimdv  3020  suctr  4404  tfrlem9  6296  lbzbi  9564  flqeqceilz  10263  ndvdsadd  11879  gcdneg  11926  bj-inf2vnlem2  13968
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