Theorem an42s

Description: Inference rearranging 4 conjuncts in antecedent. (Contributed by NM, 10-Aug-1995)

	Ref	Expression
Hypothesis	an41r3s.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜏 )
Assertion	an42s	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜃 ∧ 𝜓 ) ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		an41r3s.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜏 )
2	1	an4s	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜓 ∧ 𝜃 ) ) → 𝜏 )
3	2	ancom2s	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜃 ∧ 𝜓 ) ) → 𝜏 )