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Theorem sylbb1 226
 Description: A mixed syllogism inference from two biconditionals. (Contributed by BJ, 21-Apr-2019.)
Hypotheses
Ref Expression
sylbb1.1 (𝜑𝜓)
sylbb1.2 (𝜑𝜒)
Assertion
Ref Expression
sylbb1 (𝜓𝜒)

Proof of Theorem sylbb1
StepHypRef Expression
1 sylbb1.1 . . 3 (𝜑𝜓)
21biimpri 217 . 2 (𝜓𝜑)
3 sylbb1.2 . 2 (𝜑𝜒)
42, 3sylib 207 1 (𝜓𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195 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 196 This theorem is referenced by:  moeq  3349  fsuppmapnn0fiubex  12654  rrxcph  22988  umgrislfupgr  25789  cnvbraval  28353  ballotlemfp1  29880  finixpnum  32564  fin2so  32566  matunitlindflem1  32575  clsf2  37444  ellimcabssub0  38684  sge0iunmpt  39311  icceuelpartlem  39973  nnsum4primesodd  40212  nnsum4primesoddALTV  40213  usgrislfuspgr  40414  1wlkp1lem8  40889  elwwlks2s3  41169  eupthp1  41384
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