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Theorem trsuc2OLD 4493
 Description: Obsolete proof of suctr 4491 as of 5-Apr-2016. The successor of a transitive set is transitive. (Contributed by Scott Fenton, 21-Feb-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
trsuc2OLD

Proof of Theorem trsuc2OLD
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 andi 837 . . . 4
2 eleq2 2357 . . . . . . . 8
32biimpac 472 . . . . . . 7
43orim2i 504 . . . . . 6
5 trel 4136 . . . . . . . 8
6 orc 374 . . . . . . . 8
75, 6syl6 29 . . . . . . 7
86a1i 10 . . . . . . 7
97, 8jaod 369 . . . . . 6
104, 9syl5 28 . . . . 5
11 elsn 3668 . . . . . . 7
1211anbi2i 675 . . . . . 6
1312orbi2i 505 . . . . 5
14 elsn 3668 . . . . . 6
1514orbi2i 505 . . . . 5
1610, 13, 153imtr4g 261 . . . 4
171, 16syl5bi 208 . . 3
1817alrimivv 1622 . 2
19 df-suc 4414 . . . 4
20 treq 4135 . . . 4
2119, 20ax-mp 8 . . 3
22 dftr2 4131 . . 3
23 elun 3329 . . . . . 6
2423anbi2i 675 . . . . 5
25 elun 3329 . . . . 5
2624, 25imbi12i 316 . . . 4
27262albii 1557 . . 3
2821, 22, 273bitri 262 . 2
2918, 28sylibr 203 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wo 357   wa 358  wal 1530   wceq 1632   wcel 1696   cun 3163  csn 3653   wtr 4129   csuc 4410 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-v 2803  df-un 3170  df-in 3172  df-ss 3179  df-sn 3659  df-uni 3844  df-tr 4130  df-suc 4414
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