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Theorem 4an31 41696
Description: A rearrangement of conjuncts for a 4-right-nested conjunction. (Contributed by Alan Sare, 30-May-2018.)
Hypothesis
Ref Expression
4an31.1 ((((𝜒𝜓) ∧ 𝜑) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
4an31 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem 4an31
StepHypRef Expression
1 an31 648 . 2 (((𝜑𝜓) ∧ 𝜒) ↔ ((𝜒𝜓) ∧ 𝜑))
2 4an31.1 . 2 ((((𝜒𝜓) ∧ 𝜑) ∧ 𝜃) → 𝜏)
31, 2sylanb 584 1 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  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:  sineq0ALT  42135
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