Theorem ancom2s

Description: Inference commuting a nested conjunction in antecedent. (Contributed by NM, 24-May-2006) (Proof shortened by Wolf Lammen, 24-Nov-2012)

	Ref	Expression
Hypothesis	an12s.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
Assertion	ancom2s	⊢ ( ( 𝜑 ∧ ( 𝜒 ∧ 𝜓 ) ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		an12s.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
2		pm3.22	⊢ ( ( 𝜒 ∧ 𝜓 ) → ( 𝜓 ∧ 𝜒 ) )
3	2 1	sylan2	⊢ ( ( 𝜑 ∧ ( 𝜒 ∧ 𝜓 ) ) → 𝜃 )