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Theorem onfrALTlem4 36549
 Description: Lemma for onfrALT 36555. (Contributed by Alan Sare, 22-Jul-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
onfrALTlem4
Distinct variable group:   ,

Proof of Theorem onfrALTlem4
StepHypRef Expression
1 sbcan 3348 . 2
2 sbcel1v 3364 . . 3
3 vex 3090 . . . . 5
4 sbceqg 3807 . . . . 5
53, 4ax-mp 5 . . . 4
6 csbin 3833 . . . . . 6
7 csbconstg 3414 . . . . . . . 8
83, 7ax-mp 5 . . . . . . 7
9 csbvarg 3826 . . . . . . . 8
103, 9ax-mp 5 . . . . . . 7
118, 10ineq12i 3668 . . . . . 6
126, 11eqtri 2458 . . . . 5
13 csb0 3805 . . . . 5
1412, 13eqeq12i 2449 . . . 4
155, 14bitri 252 . . 3
162, 15anbi12i 701 . 2
171, 16bitri 252 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   wa 370   wceq 1437   wcel 1870  cvv 3087  wsbc 3305  csb 3401   cin 3441  c0 3767 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-or 371  df-an 372  df-3an 984  df-tru 1440  df-fal 1443  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-rab 2791  df-v 3089  df-sbc 3306  df-csb 3402  df-dif 3445  df-in 3449  df-ss 3456  df-nul 3768 This theorem is referenced by:  onfrALTlem1  36554  onfrALTlem1VD  36930
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