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Theorem cdleme31sn 31114
 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 3275 . . . . 5
3 nfcsb1v 3275 . . . . 5
41, 2, 3nfif 3755 . . . 4
54a1i 11 . . 3
6 breq1 4207 . . . 4
7 csbeq1a 3251 . . . 4
8 csbeq1a 3251 . . . 4
96, 7, 8ifbieq12d 3753 . . 3
105, 9csbiegf 3283 . 2
11 cdleme31sn.n . . 3
1211csbeq2i 3269 . 2
13 cdleme31sn.c . 2
1410, 12, 133eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  wnfc 2558  csb 3243  cif 3731   class class class wbr 4204  (class class class)co 6073 This theorem is referenced by:  cdleme31sn1  31115  cdleme31sn2  31123 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205
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