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Theorem sylnib 295
Description: A mixed syllogism inference from an implication and a biconditional. (Contributed by Wolf Lammen, 16-Dec-2013.)
Hypotheses
Ref Expression
sylnib.1 (φ → ¬ ψ)
sylnib.2 (ψχ)
Assertion
Ref Expression
sylnib (φ → ¬ χ)

Proof of Theorem sylnib
StepHypRef Expression
1 sylnib.1 . 2 (φ → ¬ ψ)
2 sylnib.2 . . 3 (ψχ)
32a1i 10 . 2 (φ → (ψχ))
41, 3mtbid 291 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:  sylnibr  296  ssnelpss  3613  nnc3n3p1  6278  nchoicelem1  6289
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