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Theorem sspred 25448
 Description: Another subset/predecessor class relationship. (Contributed by Scott Fenton, 6-Feb-2011.)
Assertion
Ref Expression
sspred

Proof of Theorem sspred
StepHypRef Expression
1 sseqin2 3561 . 2
2 df-pred 25440 . . . 4
32sseq1i 3373 . . 3
4 df-ss 3335 . . 3
5 in32 3554 . . . 4
65eqeq1i 2444 . . 3
73, 4, 63bitri 264 . 2
8 ineq1 3536 . . . . 5
98eqeq1d 2445 . . . 4
109biimpa 472 . . 3
11 df-pred 25440 . . . . . 6
122, 11eqeq12i 2450 . . . . 5
1312biimpri 199 . . . 4
1413eqcoms 2440 . . 3
1510, 14syl 16 . 2
161, 7, 15syl2anb 467 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   cin 3320   wss 3321  csn 3815  ccnv 4878  cima 4882  cpred 25439 This theorem is referenced by:  frmin  25518 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-v 2959  df-in 3328  df-ss 3335  df-pred 25440
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