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Theorem cdleme31sn2 30883
 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 2412 . . . . 5
31, 2cdleme31sn 30874 . . . 4
5 iffalse 3714 . . . . 5
6 cdleme32sn2.d . . . . . 6
76csbeq2i 3245 . . . . 5
85, 7syl6eq 2460 . . . 4
9 nfcvd 2549 . . . . 5
10 oveq1 6055 . . . . . 6
11 oveq2 6056 . . . . . . . 8
1211oveq1d 6063 . . . . . . 7
1312oveq2d 6064 . . . . . 6
1410, 13oveq12d 6066 . . . . 5
159, 14csbiegf 3259 . . . 4
168, 15sylan9eqr 2466 . . 3
174, 16eqtrd 2444 . 2
18 cdleme31sn2.c . 2
1917, 18syl6eqr 2462 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   wceq 1649   wcel 1721  csb 3219  cif 3707   class class class wbr 4180  (class class class)co 6048 This theorem is referenced by:  cdlemefr32sn2aw  30898  cdleme43frv1snN  30902  cdlemefr31fv1  30905  cdleme35sn2aw  30952  cdleme35sn3a  30953 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-rex 2680  df-rab 2683  df-v 2926  df-sbc 3130  df-csb 3220  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-op 3791  df-uni 3984  df-br 4181  df-iota 5385  df-fv 5429  df-ov 6051
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