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Theorem abid2f 2514
 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 2491 . . . . 5
31, 2cleqf 2513 . . . 4
4 abid 2341 . . . . . 6
54bibi2i 304 . . . . 5
65albii 1566 . . . 4
73, 6bitri 240 . . 3
8 biid 227 . . 3
97, 8mpgbir 1550 . 2
109eqcomi 2357 1
 Colors of variables: wff setvar class Syntax hints:   wb 176  wal 1540   wceq 1642   wcel 1710  cab 2339  wnfc 2476 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-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 This theorem is referenced by: (None)
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