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Theorem syl2an2r 537
Description: syl2anr 278 with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016.)
Hypotheses
Ref Expression
syl2an2r.1 (𝜑𝜓)
syl2an2r.2 ((𝜑𝜒) → 𝜃)
syl2an2r.3 ((𝜓𝜃) → 𝜏)
Assertion
Ref Expression
syl2an2r ((𝜑𝜒) → 𝜏)

Proof of Theorem syl2an2r
StepHypRef Expression
1 syl2an2r.1 . . 3 (𝜑𝜓)
2 syl2an2r.2 . . 3 ((𝜑𝜒) → 𝜃)
3 syl2an2r.3 . . 3 ((𝜓𝜃) → 𝜏)
41, 2, 3syl2an 277 . 2 ((𝜑 ∧ (𝜑𝜒)) → 𝜏)
54anabss5 520 1 ((𝜑𝜒) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  supmaxti  6408  divalglemnqt  10232
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