Theorem bnj951

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

	Ref	Expression
Hypotheses	bnj951.1	⊢ ( 𝜏 → 𝜑 )
	bnj951.2	⊢ ( 𝜏 → 𝜓 )
	bnj951.3	⊢ ( 𝜏 → 𝜒 )
	bnj951.4	⊢ ( 𝜏 → 𝜃 )
Assertion	bnj951	⊢ ( 𝜏 → ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		bnj951.1	⊢ ( 𝜏 → 𝜑 )
2		bnj951.2	⊢ ( 𝜏 → 𝜓 )
3		bnj951.3	⊢ ( 𝜏 → 𝜒 )
4		bnj951.4	⊢ ( 𝜏 → 𝜃 )
5	1 2 3	3jca	⊢ ( 𝜏 → ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )
6		df-bnj17	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) )
7	5 4 6	sylanbrc	⊢ ( 𝜏 → ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) )