Theorem bnj837

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj837.1	⊢ ( 𝜂 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )
	bnj837.2	⊢ ( 𝜒 → 𝜏 )
Assertion	bnj837	⊢ ( 𝜂 → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		bnj837.1	⊢ ( 𝜂 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )
2		bnj837.2	⊢ ( 𝜒 → 𝜏 )
3	2	3ad2ant3	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜏 )
4	1 3	sylbi	⊢ ( 𝜂 → 𝜏 )