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Theorem fnwe2lem1 30924
 Description: Lemma for fnwe2 30927. Substitution in well-ordering hypothesis. (Contributed by Stefan O'Rear, 19-Jan-2015.)
Hypotheses
Ref Expression
fnwe2.su
fnwe2.t
fnwe2.s
Assertion
Ref Expression
fnwe2lem1
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,,   ,,,,   ,
Allowed substitution hints:   ()   ()   ()   (,,)   ()

Proof of Theorem fnwe2lem1
StepHypRef Expression
1 fnwe2.s . . . 4
21ralrimiva 2881 . . 3
3 fveq2 5872 . . . . . . 7
43csbeq1d 3447 . . . . . 6
5 fvex 5882 . . . . . . 7
6 nfcv 2629 . . . . . . 7
7 fnwe2.su . . . . . . 7
85, 6, 7csbief 3465 . . . . . 6
94, 8syl6eq 2524 . . . . 5
103eqeq2d 2481 . . . . . 6
1110rabbidv 3110 . . . . 5
129, 11weeq12d 30913 . . . 4
1312cbvralv 3093 . . 3
142, 13sylibr 212 . 2
1514r19.21bi 2836 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wo 368   wa 369   wceq 1379   wcel 1767  wral 2817  crab 2821  csb 3440   class class class wbr 4453  copab 4510   wwe 4843  cfv 5594 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-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-nul 4582 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-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-rab 2826  df-v 3120  df-sbc 3337  df-csb 3441  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040  df-uni 4252  df-br 4454  df-po 4806  df-so 4807  df-fr 4844  df-we 4846  df-iota 5557  df-fv 5602 This theorem is referenced by:  fnwe2lem2  30925  fnwe2lem3  30926
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