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Theorem mpdd 40
Description: A nested modus ponens deduction. (Contributed by NM, 12-Dec-2004.)
Hypotheses
Ref Expression
mpdd.1 (𝜑 → (𝜓𝜒))
mpdd.2 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
mpdd (𝜑 → (𝜓𝜃))

Proof of Theorem mpdd
StepHypRef Expression
1 mpdd.1 . 2 (𝜑 → (𝜓𝜒))
2 mpdd.2 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
32a2d 26 . 2 (𝜑 → ((𝜓𝜒) → (𝜓𝜃)))
41, 3mpd 13 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:  mpid  41  mpdi  42  syld  44  syl6c  64  mpteqb  5288  oprabid  5564  nnmordi  6119  nnmord  6120  brecop  6226  findcard2  6376  findcard2s  6377  ordiso2  6414  zindd  8414  cau3lem  9933  climcau  10089  dvdsabseq  10151
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