Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  seinxp Unicode version

Theorem seinxp 4457
 Description: Intersection of set-like relation with cross product of its field. (Contributed by Mario Carneiro, 22-Jun-2015.)
Assertion
Ref Expression
seinxp Se Se

Proof of Theorem seinxp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 brinxp 4454 . . . . . 6
21ancoms 264 . . . . 5
32rabbidva 2598 . . . 4
43eleq1d 2151 . . 3
54ralbiia 2385 . 2
6 df-se 4116 . 2 Se
7 df-se 4116 . 2 Se
85, 6, 73bitr4i 210 1 Se Se
 Colors of variables: wff set class Syntax hints:   wb 103   wcel 1434  wral 2353  crab 2357  cvv 2610   cin 2981   class class class wbr 3805   Se wse 4112   cxp 4389 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-sep 3916  ax-pow 3968  ax-pr 3992 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-rab 2362  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-pw 3402  df-sn 3422  df-pr 3423  df-op 3425  df-br 3806  df-opab 3860  df-se 4116  df-xp 4397 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator