Theorem bnj1247

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

	Ref	Expression
Hypothesis	bnj1247.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏 ) )
Assertion	bnj1247	⊢ ( 𝜑 → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		bnj1247.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏 ) )
2		id	⊢ ( 𝜃 → 𝜃 )
3	1 2	bnj771	⊢ ( 𝜑 → 𝜃 )