Theorem rabeq 1346

Description: Equality theorem for restricted class abstractions.

Assertion

Ref	Expression
rabeq	|- (A = B -> {x e. A | ph} = {x e. B | ph})

Distinct variable group(s):   x,A   x,B

Proof of Theorem rabeq

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 |- (y e. A -> A.x y e. A)
2		ax-17 925	. 2 |- (y e. B -> A.x y e. B)
3	1, 2	rabeqf 1345	1 |- (A = B -> {x e. A | ph} = {x e. B | ph})

Syntax hints:   -> wi 2   = wceq 1091   e. wcel 1092  {crab 1204

This theorem is referenced by:  scott0 3542

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-rab 1208

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