Theorem hb3anOLD

Description: Obsolete version of hb3an as of 23-Oct-2026. (Contributed by NM, 14-Sep-2003) (Proof shortened by Wolf Lammen, 2-Jan-2018) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hbOLD.1	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
	hbOLD.2	⊢ ( 𝜓 → ∀ 𝑥 𝜓 )
	hbOLD.3	⊢ ( 𝜒 → ∀ 𝑥 𝜒 )
Assertion	hb3anOLD	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ∀ 𝑥 ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		hbOLD.1	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
2		hbOLD.2	⊢ ( 𝜓 → ∀ 𝑥 𝜓 )
3		hbOLD.3	⊢ ( 𝜒 → ∀ 𝑥 𝜒 )
4	1	nf5i	⊢ Ⅎ 𝑥 𝜑
5	2	nf5i	⊢ Ⅎ 𝑥 𝜓
6	3	nf5i	⊢ Ⅎ 𝑥 𝜒
7	4 5 6	nf3an	⊢ Ⅎ 𝑥 ( 𝜑 ∧ 𝜓 ∧ 𝜒 )
8	7	nf5ri	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ∀ 𝑥 ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )