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Theorem logic2 45856
Description: Variant of logic1 45854. (Contributed by Zhi Wang, 30-Aug-2024.)
Hypotheses
Ref Expression
pm4.71da.1 (𝜑 → (𝜓𝜒))
logic2.2 (𝜑 → ((𝜓𝜒) → (𝜃𝜏)))
Assertion
Ref Expression
logic2 (𝜑 → ((𝜓𝜃) ↔ (𝜒𝜏)))

Proof of Theorem logic2
StepHypRef Expression
1 pm4.71da.1 . 2 (𝜑 → (𝜓𝜒))
21pm4.71da 45853 . . 3 (𝜑 → (𝜓 ↔ (𝜓𝜒)))
3 logic2.2 . . 3 (𝜑 → ((𝜓𝜒) → (𝜃𝜏)))
42, 3sylbid 243 . 2 (𝜑 → (𝜓 → (𝜃𝜏)))
51, 4logic1 45854 1 (𝜑 → ((𝜓𝜃) ↔ (𝜒𝜏)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wa 399
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 210  df-an 400
This theorem is referenced by:  ralbidc  45864
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