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Theorem abid2f 2260
 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 2237 . . . . 5
31, 2cleqf 2259 . . . 4
4 abid 2083 . . . . . 6
54bibi2i 226 . . . . 5
65albii 1411 . . . 4
73, 6bitri 183 . . 3
8 biid 170 . . 3
97, 8mpgbir 1394 . 2
109eqcomi 2099 1
 Colors of variables: wff set class Syntax hints:   wb 104  wal 1294   wceq 1296   wcel 1445  cab 2081  wnfc 2222 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224 This theorem is referenced by: (None)
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