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Theorem eqerlem 6937
 Description: Lemma for eqer 6938. (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 4466 . 2
3 vex 2959 . . 3
4 nfcsb1v 3283 . . . . 5
5 nfcsb1v 3283 . . . . 5
64, 5nfeq 2579 . . . 4
7 vex 2959 . . . . . 6
8 nfv 1629 . . . . . . 7
9 vex 2959 . . . . . . . . . 10
10 nfcv 2572 . . . . . . . . . 10
11 eqer.1 . . . . . . . . . 10
129, 10, 11csbief 3292 . . . . . . . . 9
13 csbeq1 3254 . . . . . . . . 9
1412, 13syl5eqr 2482 . . . . . . . 8
1514eqeq2d 2447 . . . . . . 7
168, 15sbciegf 3192 . . . . . 6
177, 16ax-mp 8 . . . . 5
18 csbeq1a 3259 . . . . . 6
1918eqeq1d 2444 . . . . 5
2017, 19syl5bb 249 . . . 4
216, 20sbciegf 3192 . . 3
223, 21ax-mp 8 . 2
232, 22bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  cvv 2956  wsbc 3161  csb 3251   class class class wbr 4212  copab 4265 This theorem is referenced by:  eqer  6938 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267
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