Theorem bnj708

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

	Ref	Expression
Hypothesis	bnj708.1	⊢ ( 𝜃 → 𝜏 )
Assertion	bnj708	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		bnj708.1	⊢ ( 𝜃 → 𝜏 )
2		bnj645	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜃 )
3	2 1	syl	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 )