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Theorem pm2.61nii 178
Description: Inference eliminating two antecedents. (Contributed by NM, 13-Jul-2005.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 13-Nov-2012.)
Hypotheses
Ref Expression
pm2.61nii.1 (𝜑 → (𝜓𝜒))
pm2.61nii.2 𝜑𝜒)
pm2.61nii.3 𝜓𝜒)
Assertion
Ref Expression
pm2.61nii 𝜒

Proof of Theorem pm2.61nii
StepHypRef Expression
1 pm2.61nii.1 . . 3 (𝜑 → (𝜓𝜒))
2 pm2.61nii.3 . . 3 𝜓𝜒)
31, 2pm2.61d1 171 . 2 (𝜑𝜒)
4 pm2.61nii.2 . 2 𝜑𝜒)
53, 4pm2.61i 176 1 𝜒
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  ecase  982  3ecase  1434  prex  4875  nbgr0vtxlem  26155
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