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Theorem eqerlem 6137
 Description: Lemma for eqer 6138. (Contributed by NM, 17-Mar-2008.) (Proof shortened by Mario Carneiro, 6-Dec-2016.)
Hypotheses
Ref Expression
eqer.1
eqer.2
Assertion
Ref Expression
eqerlem
Distinct variable groups:   ,,   ,,   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,,,)

Proof of Theorem eqerlem
StepHypRef Expression
1 eqer.2 . . 3
21brabsb 3998 . 2
3 vex 2560 . . 3
4 nfcsb1v 2882 . . . . 5
5 nfcsb1v 2882 . . . . 5
64, 5nfeq 2185 . . . 4
7 vex 2560 . . . . . 6
8 nfv 1421 . . . . . . 7
9 vex 2560 . . . . . . . . . 10
10 nfcv 2178 . . . . . . . . . 10
11 eqer.1 . . . . . . . . . 10
129, 10, 11csbief 2891 . . . . . . . . 9
13 csbeq1 2855 . . . . . . . . 9
1412, 13syl5eqr 2086 . . . . . . . 8
1514eqeq2d 2051 . . . . . . 7
168, 15sbciegf 2794 . . . . . 6
177, 16ax-mp 7 . . . . 5
18 csbeq1a 2860 . . . . . 6
1918eqeq1d 2048 . . . . 5
2017, 19syl5bb 181 . . . 4
216, 20sbciegf 2794 . . 3
223, 21ax-mp 7 . 2
232, 22bitri 173 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243   wcel 1393  cvv 2557  wsbc 2764  csb 2852   class class class wbr 3764  copab 3817 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-sbc 2765  df-csb 2853  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819 This theorem is referenced by:  eqer  6138
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