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Theorem untsucf 25161
 Description: If a class is untangled, then so is its successor. (Contributed by Scott Fenton, 28-Feb-2011.) (Revised by Mario Carneiro, 11-Dec-2016.)
Hypothesis
Ref Expression
untsucf.1
Assertion
Ref Expression
untsucf
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem untsucf
StepHypRef Expression
1 untsucf.1 . . 3
2 nfv 1630 . . 3
31, 2nfral 2761 . 2
4 vex 2961 . . . 4
54elsuc 4652 . . 3
6 elequ1 1729 . . . . . . 7
7 elequ2 1731 . . . . . . 7
86, 7bitrd 246 . . . . . 6
98notbid 287 . . . . 5
109rspccv 3051 . . . 4
11 untelirr 25159 . . . . 5
12 eleq1 2498 . . . . . . 7
13 eleq2 2499 . . . . . . 7
1412, 13bitrd 246 . . . . . 6
1514notbid 287 . . . . 5
1611, 15syl5ibrcom 215 . . . 4
1710, 16jaod 371 . . 3
185, 17syl5bi 210 . 2
193, 18ralrimi 2789 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 359   wceq 1653   wcel 1726  wnfc 2561  wral 2707   csuc 4585 This theorem is referenced by:  dfon2lem3  25414 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-un 3327  df-sn 3822  df-suc 4589
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