Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  iota2df Unicode version

Theorem iota2df 4891
 Description: A condition that allows us to represent "the unique element such that " with a class expression . (Contributed by NM, 30-Dec-2014.)
Hypotheses
Ref Expression
iota2df.1
iota2df.2
iota2df.3
iota2df.4
iota2df.5
iota2df.6
Assertion
Ref Expression
iota2df

Proof of Theorem iota2df
StepHypRef Expression
1 iota2df.1 . 2
2 iota2df.3 . . 3
3 simpr 103 . . . 4
43eqeq2d 2051 . . 3
52, 4bibi12d 224 . 2
6 iota2df.2 . . 3
7 iota1 4881 . . 3
86, 7syl 14 . 2
9 iota2df.4 . 2
10 iota2df.6 . 2
11 iota2df.5 . . 3
12 nfiota1 4869 . . . . 5
1312a1i 9 . . . 4
1413, 10nfeqd 2192 . . 3
1511, 14nfbid 1480 . 2
161, 5, 8, 9, 10, 15vtocldf 2605 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243  wnf 1349   wcel 1393  weu 1900  wnfc 2165  cio 4865 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-sbc 2765  df-un 2922  df-sn 3381  df-pr 3382  df-uni 3581  df-iota 4867 This theorem is referenced by:  iota2d  4892  iota2  4893  riota2df  5488
 Copyright terms: Public domain W3C validator