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Theorem mpanr2 414
Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)
Hypotheses
Ref Expression
mpanr2.1 χ
mpanr2.2 ((φ (ψ χ)) → θ)
Assertion
Ref Expression
mpanr2 ((φ ψ) → θ)

Proof of Theorem mpanr2
StepHypRef Expression
1 mpanr2.1 . . 3 χ
21jctr 298 . 2 (ψ → (ψ χ))
3 mpanr2.2 . 2 ((φ (ψ χ)) → θ)
42, 3sylan2 270 1 ((φ ψ) → θ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem is referenced by:  op1steq  5747  prarloclemarch2  6402  prarloclemlt  6475  muleqadd  7411  divdivap1  7461  addltmul  7918  elfzp1b  8709  elfzm1b  8710  expp1zap  8937  expm1ap  8938
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