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Theorem wsucex 28987
 Description: Existence theorem for well-founded successor. (Contributed by Scott Fenton, 16-Jun-2018.)
Hypothesis
Ref Expression
wsucex.1
Assertion
Ref Expression
wsucex wsuc

Proof of Theorem wsucex
StepHypRef Expression
1 df-wsuc 28973 . 2 wsuc
2 wsucex.1 . . . 4
3 socnv 28799 . . . 4
42, 3syl 16 . . 3
54supexd 7913 . 2
61, 5syl5eqel 2559 1 wsuc
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1767  cvv 3113   wor 4799  ccnv 4998  csup 7900  cpred 28848  wsuccwsuc 28971 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686  ax-un 6576 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rmo 2822  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-br 4448  df-opab 4506  df-po 4800  df-so 4801  df-cnv 5007  df-sup 7901  df-wsuc 28973 This theorem is referenced by:  wsuclb  28989
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