Theorem bnj1350

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

	Ref	Expression
Hypothesis	bnj1350.1	⊢ ( 𝜒 → ∀ 𝑥 𝜒 )
Assertion	bnj1350	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ∀ 𝑥 ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		bnj1350.1	⊢ ( 𝜒 → ∀ 𝑥 𝜒 )
2		ax-5	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
3		ax-5	⊢ ( 𝜓 → ∀ 𝑥 𝜓 )
4	2 3 1	hb3an	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ∀ 𝑥 ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )