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Theorem abid2f 2410
 Description: A simplification of class abstraction. Theorem 5.2 of [Quine] p. 35. (Contributed by NM, 5-Sep-2011.) (Revised by Mario Carneiro, 7-Oct-2016.)
Hypothesis
Ref Expression
abid2f.1
Assertion
Ref Expression
abid2f

Proof of Theorem abid2f
StepHypRef Expression
1 abid2f.1 . . . . 5
2 nfab1 2387 . . . . 5
31, 2cleqf 2409 . . . 4
4 abid 2241 . . . . . 6
54bibi2i 306 . . . . 5
65albii 1554 . . . 4
73, 6bitri 242 . . 3
8 biid 229 . . 3
97, 8mpgbir 1544 . 2
109eqcomi 2257 1
 Colors of variables: wff set class Syntax hints:   wb 178  wal 1532   wceq 1619   wcel 1621  cab 2239  wnfc 2372 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374
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