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Theorem rabeq2i 2856
 Description: Inference rule from equality of a class variable and a restricted class abstraction. (Contributed by NM, 16-Feb-2004.)
Hypothesis
Ref Expression
rabeqi.1 A = {x B φ}
Assertion
Ref Expression
rabeq2i (x A ↔ (x B φ))

Proof of Theorem rabeq2i
StepHypRef Expression
1 rabeqi.1 . . 3 A = {x B φ}
21eleq2i 2417 . 2 (x Ax {x B φ})
3 rabid 2787 . 2 (x {x B φ} ↔ (x B φ))
42, 3bitri 240 1 (x A ↔ (x B φ))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358   = wceq 1642   ∈ wcel 1710  {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-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-rab 2623 This theorem is referenced by:  fvmptss  5705
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