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Theorem rabid2f 23967
 Description: An "identity" law for restricted class abstraction. (Contributed by NM, 9-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.) (Revised by Thierry Arnoux, 13-Mar-2017.)
Hypothesis
Ref Expression
rabid2f.1
Assertion
Ref Expression
rabid2f

Proof of Theorem rabid2f
StepHypRef Expression
1 rabid2f.1 . . . 4
21abeq2f 23960 . . 3
3 pm4.71 612 . . . 4
43albii 1575 . . 3
52, 4bitr4i 244 . 2
6 df-rab 2714 . . 3
76eqeq2i 2446 . 2
8 df-ral 2710 . 2
95, 7, 83bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wceq 1652   wcel 1725  cab 2422  wnfc 2559  wral 2705  crab 2709 This theorem is referenced by:  funcnvmptOLD  24082  funcnvmpt  24083 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rab 2714
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