Theorem rspec 2679

Description: Specialization rule for restricted quantification. (Contributed by NM, 19-Nov-1994.)

Hypothesis

Ref	Expression
rspec.1	⊢ ∀x ∈ A φ

Assertion

Ref	Expression
rspec	⊢ (x ∈ A → φ)

Proof of Theorem rspec

Step	Hyp	Ref	Expression
1		rspec.1	. 2 ⊢ ∀x ∈ A φ
2		rsp 2675	. 2 ⊢ (∀x ∈ A φ → (x ∈ A → φ))
3	1, 2	ax-mp 5	1 ⊢ (x ∈ A → φ)

Syntax hints:   → wi 4   ∈ wcel 1710  ∀wral 2615

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-ral 2620

This theorem is referenced by:  rspec2  2714  vtoclri  2930