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Theorem syl2an2 559
Description: syl2an 283 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 283 . 2 ((𝜑 ∧ (𝜒𝜑)) → 𝜏)
54anabss7 548 1 ((𝜒𝜑) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  qbtwnz  9338  sizef1rn  9813  isumrblem  10337  divalgmod  10471  gcdsupex  10493  gcdsupcl  10494  cncongr2  10630  isprm3  10644
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