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Theorem syl2an2 870
Description: syl2an 492 with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016.)
Hypotheses
Ref Expression
syl2an2.1 (𝜑𝜓)
syl2an2.2 ((𝜒𝜑) → 𝜃)
syl2an2.3 ((𝜓𝜃) → 𝜏)
Assertion
Ref Expression
syl2an2 ((𝜒𝜑) → 𝜏)

Proof of Theorem syl2an2
StepHypRef Expression
1 syl2an2.1 . . 3 (𝜑𝜓)
2 syl2an2.2 . . 3 ((𝜒𝜑) → 𝜃)
3 syl2an2.3 . . 3 ((𝜓𝜃) → 𝜏)
41, 2, 3syl2an 492 . 2 ((𝜑 ∧ (𝜒𝜑)) → 𝜏)
54anabss7 857 1 ((𝜒𝜑) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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 195  df-an 384
This theorem is referenced by:  elrab3t  3329  reusv2lem3  4791  fvmpt2d  6186  fmptco  6287  fseqdom  8709  hashimarn  13039  divalgmod  14915  lcmfunsnlem2  15139  lcmflefac  15147  cncongr2  15168  esum2dlem  29274  bj-restsnss  32000  bj-restsnss2  32001  k0004lem3  37250  usgr1v  40463  cplgr2vpr  40636  vtxdg0e  40670  wlknewwlksn  41065  wwlksnextwrd  41084  wwlksnwwlksnon  41102  clwlkclwwlklem2a4  41187
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