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Theorem bj-csbsnlem 34613
 Description: Lemma for bj-csbsn 34614 (in this lemma, cannot occur in ). (Contributed by BJ, 6-Oct-2018.) (New usage is discouraged.)
Assertion
Ref Expression
bj-csbsnlem
Distinct variable group:   ,

Proof of Theorem bj-csbsnlem
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 abid 2444 . . . 4
2 df-sbc 3328 . . . 4
3 clelab 2601 . . . . 5
4 elsn 4046 . . . . . . 7
54anbi2i 694 . . . . . 6
65exbii 1668 . . . . 5
7 eqeq2 2472 . . . . . . . 8
87pm5.32i 637 . . . . . . 7
98exbii 1668 . . . . . 6
10 19.41v 1772 . . . . . 6
11 simpr 461 . . . . . . 7
12 eqvisset 3117 . . . . . . . . 9
13 elisset 3120 . . . . . . . . 9
1412, 13syl 16 . . . . . . . 8
1514ancri 552 . . . . . . 7
1611, 15impbii 188 . . . . . 6
179, 10, 163bitri 271 . . . . 5
183, 6, 173bitri 271 . . . 4
191, 2, 183bitri 271 . . 3
20 df-csb 3431 . . . 4
2120eleq2i 2535 . . 3
22 elsn 4046 . . 3
2319, 21, 223bitr4i 277 . 2
2423eqriv 2453 1
 Colors of variables: wff setvar class Syntax hints:   wa 369   wceq 1395  wex 1613   wcel 1819  cab 2442  cvv 3109  wsbc 3327  csb 3430  csn 4032 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328  df-csb 3431  df-sn 4033 This theorem is referenced by:  bj-csbsn  34614
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