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Theorem sspred 5407
 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 3687 . 2
2 df-pred 5399 . . . 4
32sseq1i 3494 . . 3
4 df-ss 3456 . . 3
5 in32 3680 . . . 4
65eqeq1i 2436 . . 3
73, 4, 63bitri 274 . 2
8 ineq1 3663 . . . . 5
98eqeq1d 2431 . . . 4
109biimpa 486 . . 3
11 df-pred 5399 . . . . . 6
122, 11eqeq12i 2449 . . . . 5
1312biimpri 209 . . . 4
1413eqcoms 2441 . . 3
1510, 14syl 17 . 2
161, 7, 15syl2anb 481 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wceq 1437   cin 3441   wss 3442  csn 4002  ccnv 4853  cima 4857  cpred 5398 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-v 3089  df-in 3449  df-ss 3456  df-pred 5399 This theorem is referenced by:  frmin  30267
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