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Theorem cdleme31sn 29258
 Description: Part of proof of Lemma E in [Crawley] p. 113. (Contributed by NM, 26-Feb-2013.)
Hypotheses
Ref Expression
cdleme31sn.n
cdleme31sn.c
Assertion
Ref Expression
cdleme31sn
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem cdleme31sn
StepHypRef Expression
1 nfv 1629 . . . . 5
2 nfcsb1v 3041 . . . . 5
3 nfcsb1v 3041 . . . . 5
41, 2, 3nfif 3494 . . . 4
54a1i 12 . . 3
6 breq1 3923 . . . 4
7 csbeq1a 3017 . . . 4
8 csbeq1a 3017 . . . 4
96, 7, 8ifbieq12d 3492 . . 3
105, 9csbiegf 3049 . 2
11 cdleme31sn.n . . 3
1211csbeq2i 3035 . 2
13 cdleme31sn.c . 2
1410, 12, 133eqtr4g 2310 1
 Colors of variables: wff set class Syntax hints:   wi 6   wceq 1619   wcel 1621  wnfc 2372  csb 3009  cif 3470   class class class wbr 3920  (class class class)co 5710 This theorem is referenced by:  cdleme31sn1  29259  cdleme31sn2  29267 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-rab 2516  df-v 2729  df-sbc 2922  df-csb 3010  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-br 3921
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