Theorem bnj1352

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

	Ref	Expression
Hypothesis	bnj1352.1	⊢ ( 𝜓 → ∀ 𝑥 𝜓 )
Assertion	bnj1352	⊢ ( ( 𝜑 ∧ 𝜓 ) → ∀ 𝑥 ( 𝜑 ∧ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		bnj1352.1	⊢ ( 𝜓 → ∀ 𝑥 𝜓 )
2		ax-5	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
3	2 1	hban	⊢ ( ( 𝜑 ∧ 𝜓 ) → ∀ 𝑥 ( 𝜑 ∧ 𝜓 ) )