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Theorem mpid 42
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 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:  mp2d  47  pm2.43a  51  embantd  56  mpan2d  424  ceqsalt  2686  rspcimdv  2764  fvimacnv  5503  riotass2  5724  pr2ne  7016  0mnnnnn0  8977  caucvgre  10721  climcn1  11045  climcn2  11046  gcdaddm  11599  dvdsgcd  11627  coprmgcdb  11696  nprm  11731  uniopn  12095  metcnp3  12607  cncfco  12674
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