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Theorem elpw131c 4149
 Description: Membership in 1 1 1 1c (Contributed by SF, 14-Jan-2015.)
Assertion
Ref Expression
elpw131c 1 1 1 1c
Distinct variable group:   ,

Proof of Theorem elpw131c
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elpw1 4144 . 2 1 1 1 1c 1 1 1c
2 df-rex 2620 . . . 4 1 1 1c 1 1 1c
3 elpw121c 4148 . . . . . . 7 1 1 1c
43anbi1i 676 . . . . . 6 1 1 1c
5 19.41v 1901 . . . . . 6
64, 5bitr4i 243 . . . . 5 1 1 1c
76exbii 1582 . . . 4 1 1 1c
82, 7bitri 240 . . 3 1 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 1 1c
171, 16bitri 240 1 1 1 1 1c
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  wrex 2615  csn 3737  1cc1c 4134  1 cpw1 4135 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 This theorem is referenced by:  elpw141c  4150  nnsucelrlem1  4424  ltfinex  4464  eqpw1relk  4479  ncfinraiselem2  4480  ncfinlowerlem1  4482  eqtfinrelk  4486  oddfinex  4504  nnpweqlem1  4522  srelk  4524
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