Theorem 4an31

Description: A rearrangement of conjuncts for a 4-right-nested conjunction. (Contributed by Alan Sare, 30-May-2018)

	Ref	Expression
Hypothesis	4an31.1	⊢ ( ( ( ( 𝜒 ∧ 𝜓 ) ∧ 𝜑 ) ∧ 𝜃 ) → 𝜏 )
Assertion	4an31	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		4an31.1	⊢ ( ( ( ( 𝜒 ∧ 𝜓 ) ∧ 𝜑 ) ∧ 𝜃 ) → 𝜏 )
2		an31	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ↔ ( ( 𝜒 ∧ 𝜓 ) ∧ 𝜑 ) )
3	2 1	sylanb	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )