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Theorem mpid 41
Description: A nested modus ponens deduction. (Contributed by NM, 14-Dec-2004.)
Hypotheses
Ref Expression
mpid.1 (𝜑𝜒)
mpid.2 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
mpid (𝜑 → (𝜓𝜃))

Proof of Theorem mpid
StepHypRef Expression
1 mpid.1 . . 3 (𝜑𝜒)
21a1d 22 . 2 (𝜑 → (𝜓𝜒))
3 mpid.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:  mp2d  46  pm2.43a  50  embantd  55  mpan2d  419  ceqsalt  2645  rspcimdv  2723  fvimacnv  5398  riotass2  5616  pr2ne  6799  0mnnnnn0  8675  caucvgre  10378  climcn1  10660  climcn2  10661  gcdaddm  11055  dvdsgcd  11081  coprmgcdb  11150  nprm  11185
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