Theorem rspec 1246

Description: Specialization rule for restricted quantification.

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		ra4 1243	. 2 ⊢ (∀x ∈ A φ → (x ∈ A → φ))
3	1, 2	ax-mp 6	1 ⊢ (x ∈ A → φ)

Syntax hints:   → wi 2   ∈ wcel 1092  ∀wral 1201

This theorem is referenced by:  rspec2 1267  vtoclri 1393  indstr 4611

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673

This theorem depends on definitions:  df-bi 128  df-ral 1205

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