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Theorem ssrab2 3351

Description: Subclass relation for a restricted class. (Contributed by NM, 19-Mar-1997.)

**Assertion**
Ref	Expression
ssrab2	⊢ {x ∈ A ∣ φ} ⊆ A

**Proof of Theorem ssrab2**
Step	Hyp	Ref	Expression
1		df-rab 2623	. 2 ⊢ {x ∈ A ∣ φ} = {x ∣ (x ∈ A ∧ φ)}
2		ssab2 3350	. 2 ⊢ {x ∣ (x ∈ A ∧ φ)} ⊆ A
3	1, 2	eqsstri 3301	1 ⊢ {x ∈ A ∣ φ} ⊆ A

Colors of variables: wff setvar class

Syntax hints: ∧ wa 358 ∈ wcel 1710 {cab 2339 {crab 2618 ⊆ wss 3257

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334

This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rab 2623 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259

This theorem is referenced by: iinrab2 4029 riinrab 4041 reiotacl 4364 nenpw1pwlem2 6085