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Theorem cdleme31sn2 31123
 Description: Part of proof of Lemma E in [Crawley] p. 113. (Contributed by NM, 26-Feb-2013.)
Hypotheses
Ref Expression
cdleme32sn2.d
cdleme31sn2.n
cdleme31sn2.c
Assertion
Ref Expression
cdleme31sn2
Distinct variable groups:   ,   ,   ,   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem cdleme31sn2
StepHypRef Expression
1 cdleme31sn2.n . . . . 5
2 eqid 2435 . . . . 5
31, 2cdleme31sn 31114 . . . 4
5 iffalse 3738 . . . . 5
6 cdleme32sn2.d . . . . . 6
76csbeq2i 3269 . . . . 5
85, 7syl6eq 2483 . . . 4
9 nfcvd 2572 . . . . 5
10 oveq1 6080 . . . . . 6
11 oveq2 6081 . . . . . . . 8
1211oveq1d 6088 . . . . . . 7
1312oveq2d 6089 . . . . . 6
1410, 13oveq12d 6091 . . . . 5
159, 14csbiegf 3283 . . . 4
168, 15sylan9eqr 2489 . . 3
174, 16eqtrd 2467 . 2
18 cdleme31sn2.c . 2
1917, 18syl6eqr 2485 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   wceq 1652   wcel 1725  csb 3243  cif 3731   class class class wbr 4204  (class class class)co 6073 This theorem is referenced by:  cdlemefr32sn2aw  31138  cdleme43frv1snN  31142  cdlemefr31fv1  31145  cdleme35sn2aw  31192  cdleme35sn3a  31193 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-rex 2703  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-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076
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