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Theorem drex1 1676
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 1603 . . . 4
2 drex1.1 . . . . 5
3 ax-4 1397 . . . . . 6
43biantrurd 289 . . . . 5
52, 4bitr2d 178 . . . 4
61, 5exbidh 1502 . . 3
7 ax11e 1674 . . . 4
87sps 1427 . . 3
96, 8sylbird 159 . 2
10 hbae 1603 . . . 4
11 equcomi 1589 . . . . . . 7
1211sps 1427 . . . . . 6
1312biantrurd 289 . . . . 5
1413, 2bitr3d 179 . . . 4
1510, 14exbidh 1502 . . 3
16 ax11e 1674 . . . . 5
1716sps 1427 . . . 4
1817alequcoms 1406 . . 3
1915, 18sylbird 159 . 2
209, 19impbid 120 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   wceq 1242  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  drsb1  1677  exdistrfor  1678  copsexg  3972
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