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Theorem rabeq 2853
 Description: Equality theorem for restricted class abstractions. (Contributed by NM, 15-Oct-2003.)
Assertion
Ref Expression
rabeq (A = B → {x A φ} = {x B φ})
Distinct variable groups:   x,A   x,B
Allowed substitution hint:   φ(x)

Proof of Theorem rabeq
StepHypRef Expression
1 nfcv 2489 . 2 xA
2 nfcv 2489 . 2 xB
31, 2rabeqf 2852 1 (A = B → {x A φ} = {x B φ})
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  {crab 2618 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-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 This theorem is referenced by:  rabeqbidv  2854  rabeqbidva  2855  ifeq1  3666  ifeq2  3667
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