Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  cbviota Structured version   Unicode version

Theorem cbviota 5415
 Description: Change bound variables in a description binder. (Contributed by Andrew Salmon, 1-Aug-2011.)
Hypotheses
Ref Expression
cbviota.1
cbviota.2
cbviota.3
Assertion
Ref Expression
cbviota

Proof of Theorem cbviota
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 nfv 1629 . . . . . 6
2 nfs1v 2181 . . . . . . 7
3 nfv 1629 . . . . . . 7
42, 3nfbi 1856 . . . . . 6
5 sbequ12 1944 . . . . . . 7
6 equequ1 1696 . . . . . . 7
75, 6bibi12d 313 . . . . . 6
81, 4, 7cbval 1982 . . . . 5
9 cbviota.2 . . . . . . . 8
109nfsb 2184 . . . . . . 7
11 nfv 1629 . . . . . . 7
1210, 11nfbi 1856 . . . . . 6
13 nfv 1629 . . . . . 6
14 sbequ 2138 . . . . . . . 8
15 cbviota.3 . . . . . . . . 9
16 cbviota.1 . . . . . . . . 9
1715, 16sbie 2122 . . . . . . . 8
1814, 17syl6bb 253 . . . . . . 7
19 equequ1 1696 . . . . . . 7
2018, 19bibi12d 313 . . . . . 6
2112, 13, 20cbval 1982 . . . . 5
228, 21bitri 241 . . . 4
2322abbii 2547 . . 3
2423unieqi 4017 . 2
25 dfiota2 5411 . 2
26 dfiota2 5411 . 2
2724, 25, 263eqtr4i 2465 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549  wnf 1553   wceq 1652  wsb 1658  cab 2421  cuni 4007  cio 5408 This theorem is referenced by:  cbviotav  5416  fvopab5  6526  cbvriota  6552 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-sn 3812  df-uni 4008  df-iota 5410
 Copyright terms: Public domain W3C validator