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Theorem abeq2i 2460
 Description: Equality of a class variable and a class abstraction (inference rule). (Contributed by NM, 3-Apr-1996.)
Hypothesis
Ref Expression
abeqi.1 A = {x φ}
Assertion
Ref Expression
abeq2i (x Aφ)

Proof of Theorem abeq2i
StepHypRef Expression
1 abeqi.1 . . 3 A = {x φ}
21eleq2i 2417 . 2 (x Ax {x φ})
3 abid 2341 . 2 (x {x φ} ↔ φ)
42, 3bitri 240 1 (x Aφ)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   = wceq 1642   ∈ wcel 1710  {cab 2339 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 This theorem is referenced by:  rabid  2787  vex  2862  csbco  3145  csbnestgf  3184  pwss  3736  elsn  3748  snsspw  3877  1cex  4142  elp6  4263  unipw1  4325  phi011lem1  4598  fconstopab  4815  fvfullfunlem3  5863  fvfullfun  5864  pmvalg  6010  enpw1pw  6075
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