Theorem bnj1219

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

	Ref	Expression
Hypotheses	bnj1219.1	⊢ ( 𝜒 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜁 ) )
	bnj1219.2	⊢ ( 𝜃 ↔ ( 𝜒 ∧ 𝜏 ∧ 𝜂 ) )
Assertion	bnj1219	⊢ ( 𝜃 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bnj1219.1	⊢ ( 𝜒 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜁 ) )
2		bnj1219.2	⊢ ( 𝜃 ↔ ( 𝜒 ∧ 𝜏 ∧ 𝜂 ) )
3	1	simp2bi	⊢ ( 𝜒 → 𝜓 )
4	2 3	bnj835	⊢ ( 𝜃 → 𝜓 )