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Theorem drex1 1721
 Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). (Contributed by NM, 27-Feb-2005.) (Revised by NM, 3-Feb-2015.)
Hypothesis
Ref Expression
drex1.1
Assertion
Ref Expression
drex1

Proof of Theorem drex1
StepHypRef Expression
1 hbae 1648 . . . 4
2 drex1.1 . . . . 5
3 ax-4 1441 . . . . . 6
43biantrurd 299 . . . . 5
52, 4bitr2d 187 . . . 4
61, 5exbidh 1546 . . 3
7 ax11e 1719 . . . 4
87sps 1471 . . 3
96, 8sylbird 168 . 2
10 hbae 1648 . . . 4
11 equcomi 1633 . . . . . . 7
1211sps 1471 . . . . . 6
1312biantrurd 299 . . . . 5
1413, 2bitr3d 188 . . . 4
1510, 14exbidh 1546 . . 3
16 ax11e 1719 . . . . 5
1716sps 1471 . . . 4
1817alequcoms 1450 . . 3
1915, 18sylbird 168 . 2
209, 19impbid 127 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283   wceq 1285  wex 1422 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468 This theorem depends on definitions:  df-bi 115 This theorem is referenced by:  drsb1  1722  exdistrfor  1723  copsexg  4027
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