Theorem bnj1254

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj1254.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏 ) )
Assertion	bnj1254	⊢ ( 𝜑 → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		bnj1254.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏 ) )
2		id	⊢ ( 𝜏 → 𝜏 )
3	2	bnj708	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏 ) → 𝜏 )
4	1 3	sylbi	⊢ ( 𝜑 → 𝜏 )