Theorem bnj835

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

	Ref	Expression
Hypotheses	bnj835.1	⊢ ( 𝜂 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )
	bnj835.2	⊢ ( 𝜑 → 𝜏 )
Assertion	bnj835	⊢ ( 𝜂 → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		bnj835.1	⊢ ( 𝜂 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )
2		bnj835.2	⊢ ( 𝜑 → 𝜏 )
3	2	3ad2ant1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜏 )
4	1 3	sylbi	⊢ ( 𝜂 → 𝜏 )