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Theorem syl2an2 871
 Description: syl2an 493 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 493 . 2 ((𝜑 ∧ (𝜒𝜑)) → 𝜏)
54anabss7 858 1 ((𝜒𝜑) → 𝜏)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383 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  df-an 385 This theorem is referenced by:  elrab3t  3330  reusv2lem3  4797  fvmpt2d  6202  fmptco  6303  fseqdom  8732  hashimarn  13085  divalgmod  14967  lcmfunsnlem2  15191  lcmflefac  15199  cncongr2  15220  esum2dlem  29481  bj-restsnss  32217  bj-restsnss2  32218  k0004lem3  37467  usgr1v  40482  cplgr2vpr  40655  vtxdg0e  40689  wlknewwlksn  41084  wwlksnextwrd  41103  wwlksnwwlksnon  41121  clwlkclwwlklem2a4  41206
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