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Theorem mpii 46
Description: A doubly nested modus ponens inference. (Contributed by NM, 31-Dec-1993.) (Proof shortened by Wolf Lammen, 31-Jul-2012.)
Hypotheses
Ref Expression
mpii.1 𝜒
mpii.2 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
mpii (𝜑 → (𝜓𝜃))

Proof of Theorem mpii
StepHypRef Expression
1 mpii.1 . . 3 𝜒
21a1i 11 . 2 (𝜓𝜒)
3 mpii.2 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
42, 3mpdi 45 1 (𝜑 → (𝜓𝜃))
Colors of variables: wff setvar 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:  intmin  4467  dfiin2g  4524  ssorduni  6939  suceloni  6967  lublecllem  16920  irredmul  18641  opnneiid  20853  isufil2  21635  mdbr3  29026  mdbr4  29027  dmdbr5  29037  filnetlem4  32053  iunord  41740
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