Theorem an4s

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

	Ref	Expression
Hypothesis	an4s.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜏 )
Assertion	an4s	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜓 ∧ 𝜃 ) ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		an4s.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜏 )
2		an4	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜓 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) )
3	2 1	sylbi	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜓 ∧ 𝜃 ) ) → 𝜏 )