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

Theorem iotabi 5566
 Description: Equivalence theorem for descriptions. (Contributed by Andrew Salmon, 30-Jun-2011.)
Assertion
Ref Expression
iotabi

Proof of Theorem iotabi
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 abbi 2598 . . . . . 6
21biimpi 194 . . . . 5
32eqeq1d 2469 . . . 4
43abbidv 2603 . . 3
54unieqd 4261 . 2
6 df-iota 5557 . 2
7 df-iota 5557 . 2
85, 6, 73eqtr4g 2533 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184  wal 1377   wceq 1379  cab 2452  csn 4033  cuni 4251  cio 5555 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rex 2823  df-uni 4252  df-iota 5557 This theorem is referenced by:  iotabidv  5578  iotabii  5579  eusvobj1  6289  iotasbcq  31246  fourierdlem89  31819  fourierdlem90  31820  fourierdlem91  31821  fourierdlem96  31826  fourierdlem97  31827  fourierdlem98  31828  fourierdlem99  31829  fourierdlem100  31830  fourierdlem104  31834  fourierdlem112  31842
 Copyright terms: Public domain W3C validator