Theorem r19.21be

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 21-Nov-1994)

	Ref	Expression
Hypothesis	r19.21be.1	⊢ ( 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜓 )
Assertion	r19.21be	⊢ ∀ 𝑥 ∈ 𝐴 ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		r19.21be.1	⊢ ( 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜓 )
2	1	r19.21bi	⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) → 𝜓 )
3	2	expcom	⊢ ( 𝑥 ∈ 𝐴 → ( 𝜑 → 𝜓 ) )
4	3	rgen	⊢ ∀ 𝑥 ∈ 𝐴 ( 𝜑 → 𝜓 )