New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  elpw11c Unicode version

Theorem elpw11c 4147
 Description: Membership in 1 1c (Contributed by SF, 13-Jan-2015.)
Assertion
Ref Expression
elpw11c 1 1c
Distinct variable group:   ,

Proof of Theorem elpw11c
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elpw1 4144 . 2 1 1c 1c
2 df-rex 2620 . . 3 1c 1c
3 el1c 4139 . . . . . 6 1c
43anbi1i 676 . . . . 5 1c
5 19.41v 1901 . . . . 5
64, 5bitr4i 243 . . . 4 1c
76exbii 1582 . . 3 1c
82, 7bitri 240 . 2 1c
9 excom 1741 . . 3
10 snex 4111 . . . . 5
11 sneq 3744 . . . . . 6
1211eqeq2d 2364 . . . . 5
1310, 12ceqsexv 2894 . . . 4
1413exbii 1582 . . 3
159, 14bitri 240 . 2
161, 8, 153bitri 262 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-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 This theorem is referenced by:  elpw121c  4148  insklem  4304  ncfinraiselem2  4480  ncfinlowerlem1  4482  eqtfinrelk  4486  evenodddisjlem1  4515  nnpweqlem1  4522  sfintfinlem1  4531  tfinnnlem1  4533  df1st2  4738  dfswap2  4741
 Copyright terms: Public domain W3C validator