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Theorem eqerlem 7345
 Description: Lemma for eqer 7346. (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 4748 . 2
3 vex 3098 . . 3
4 nfcsb1v 3436 . . . . 5
5 nfcsb1v 3436 . . . . 5
64, 5nfeq 2616 . . . 4
7 vex 3098 . . . . . 6
8 nfv 1694 . . . . . . 7
9 vex 3098 . . . . . . . . . 10
10 eqer.1 . . . . . . . . . 10
119, 10csbie 3446 . . . . . . . . 9
12 csbeq1 3423 . . . . . . . . 9
1311, 12syl5eqr 2498 . . . . . . . 8
1413eqeq2d 2457 . . . . . . 7
158, 14sbciegf 3345 . . . . . 6
167, 15ax-mp 5 . . . . 5
17 csbeq1a 3429 . . . . . 6
1817eqeq1d 2445 . . . . 5
1916, 18syl5bb 257 . . . 4
206, 19sbciegf 3345 . . 3
213, 20ax-mp 5 . 2
222, 21bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1383   wcel 1804  cvv 3095  wsbc 3313  csb 3420   class class class wbr 4437  copab 4494 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pr 4676 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-eu 2272  df-mo 2273  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3097  df-sbc 3314  df-csb 3421  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-br 4438  df-opab 4496 This theorem is referenced by:  eqer  7346
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