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Theorem sylnibr 296
 Description: A mixed syllogism inference from an implication and a biconditional. Useful for substituting a consequent with a definition. (Contributed by Wolf Lammen, 16-Dec-2013.)
Hypotheses
Ref Expression
sylnibr.1 (φ → ¬ ψ)
sylnibr.2 (χψ)
Assertion
Ref Expression
sylnibr (φ → ¬ χ)

Proof of Theorem sylnibr
StepHypRef Expression
1 sylnibr.1 . 2 (φ → ¬ ψ)
2 sylnibr.2 . . 3 (χψ)
32bicomi 193 . 2 (ψχ)
41, 3sylnib 295 1 (φ → ¬ χ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 177 This theorem is referenced by:  ncfinraise  4481  tfinltfin  4501  sfindbl  4530  tfinnn  4534  vfinncvntsp  4549  nnc3n3p1  6278  nnc3n3p2  6279  nnc3p1n3p2  6280  nchoicelem2  6290
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