Theorem 4an4132

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

	Ref	Expression
Hypothesis	4an4132.1	⊢ ( ( ( ( 𝜃 ∧ 𝜒 ) ∧ 𝜓 ) ∧ 𝜑 ) → 𝜏 )
Assertion	4an4132	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		4an4132.1	⊢ ( ( ( ( 𝜃 ∧ 𝜒 ) ∧ 𝜓 ) ∧ 𝜑 ) → 𝜏 )
2		simpr	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜃 )
3		simplr	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜒 )
4	2 3	jca	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → ( 𝜃 ∧ 𝜒 ) )
5		simpllr	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜓 )
6		simplll	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜑 )
7	4 5 6 1	syl21anc	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )