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Theorem syl7bi 245
 Description: A mixed syllogism inference from a doubly nested implication and a biconditional. (Contributed by NM, 14-May-1993.)
Hypotheses
Ref Expression
syl7bi.1 (𝜑𝜓)
syl7bi.2 (𝜒 → (𝜃 → (𝜓𝜏)))
Assertion
Ref Expression
syl7bi (𝜒 → (𝜃 → (𝜑𝜏)))

Proof of Theorem syl7bi
StepHypRef Expression
1 syl7bi.1 . . 3 (𝜑𝜓)
21biimpi 206 . 2 (𝜑𝜓)
3 syl7bi.2 . 2 (𝜒 → (𝜃 → (𝜓𝜏)))
42, 3syl7 74 1 (𝜒 → (𝜃 → (𝜑𝜏)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196 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 197 This theorem is referenced by:  3jao  1537  nfimt  1970  rspct  3442  zfpair  5053  gruen  9826  axpre-sup  10182  nn0lt2  11632  fzofzim  12709  ndvdssub  15335  alexsubALT  22056  clwlkclwwlklem2a  27121  erclwwlktr  27145  erclwwlkntr  27202  dfon2lem8  32000  prtlem15  34664  prtlem18  34666
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