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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
sylnib.2
Assertion
Ref Expression
sylnib

Proof of Theorem sylnib
StepHypRef Expression
1 sylnib.1 . 2
2 sylnib.2 . . 3
32a1i 10 . 2
41, 3mtbid 291 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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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