Theorem or32dd 33896

Description: A rearrangement of disjuncts, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)

Hypothesis

Ref	Expression
or32dd.1	⊢ (𝜑 → (𝜓 → ((𝜒 ∨ 𝜃) ∨ 𝜏)))

Assertion

Ref	Expression
or32dd	⊢ (𝜑 → (𝜓 → ((𝜒 ∨ 𝜏) ∨ 𝜃)))

Proof of Theorem or32dd

Step	Hyp	Ref	Expression
1		or32dd.1	. 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∨ 𝜃) ∨ 𝜏)))
2		or32 549	. 2 ⊢ (((𝜒 ∨ 𝜏) ∨ 𝜃) ↔ ((𝜒 ∨ 𝜃) ∨ 𝜏))
3	1, 2	syl6ibr 242	1 ⊢ (𝜑 → (𝜓 → ((𝜒 ∨ 𝜏) ∨ 𝜃)))

Syntax hints:   → wi 4   ∨ wo 383

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 197  df-or 385

This theorem is referenced by:  mpt2bi123f  33971  mptbi12f  33975  ac6s6  33980