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Theorem sylancl2 31582
Description: Shortens 5 proofs. (Contributed by BJ, 25-Apr-2019.)
Hypotheses
Ref Expression
sylancl2.1 (𝜑𝜓)
sylancl2.2 𝜒
sylancl2.3 ((𝜓𝜒) ↔ 𝜃)
Assertion
Ref Expression
sylancl2 (𝜑𝜃)

Proof of Theorem sylancl2
StepHypRef Expression
1 sylancl2.1 . 2 (𝜑𝜓)
2 sylancl2.2 . 2 𝜒
3 sylancl2.3 . . 3 ((𝜓𝜒) ↔ 𝜃)
43biimpi 204 . 2 ((𝜓𝜒) → 𝜃)
51, 2, 4sylancl 692 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  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: (None)
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