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Theorem elpw121c 4148
 Description: Membership in 1 1 1c (Contributed by SF, 13-Jan-2015.)
Assertion
Ref Expression
elpw121c 1 1 1c
Distinct variable group:   ,

Proof of Theorem elpw121c
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elpw1 4144 . 2 1 1 1c 1 1c
2 df-rex 2620 . . . 4 1 1c 1 1c
3 elpw11c 4147 . . . . . . 7 1 1c
43anbi1i 676 . . . . . 6 1 1c
5 19.41v 1901 . . . . . 6
64, 5bitr4i 243 . . . . 5 1 1c
76exbii 1582 . . . 4 1 1c
82, 7bitri 240 . . 3 1 1c
9 excom 1741 . . . 4
10 snex 4111 . . . . . 6
11 sneq 3744 . . . . . . 7
1211eqeq2d 2364 . . . . . 6
1310, 12ceqsexv 2894 . . . . 5
1413exbii 1582 . . . 4
159, 14bitri 240 . . 3
168, 15bitri 240 . 2 1 1c
171, 16bitri 240 1 1 1 1c
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  wrex 2615  csn 3737  1cc1c 4134  1 cpw1 4135 This theorem is referenced by:  elpw131c  4149  opkelimagekg  4271  ndisjrelk  4323  eqpwrelk  4478  ncfinraiselem2  4480  ncfinlowerlem1  4482  eqtfinrelk  4486  evenfinex  4503  oddfinex  4504  evenodddisjlem1  4515  nnadjoinlem1  4519  nnpweqlem1  4522  srelk  4524  tfinnnlem1  4533  spfinex  4537  dfop2lem1  4573  setconslem2  4724 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-sn 4087 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-pw 3724  df-sn 3741  df-1c 4136  df-pw1 4137
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