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Theorem iotaequ 27644
Description: Theorem *14.2 in [WhiteheadRussell] p. 189. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
iotaequ  |-  ( iota
x x  =  y )  =  y
Distinct variable group:    x, y

Proof of Theorem iotaequ
StepHypRef Expression
1 iotaval 5458 . 2  |-  ( A. x ( x  =  y  <->  x  =  y
)  ->  ( iota x x  =  y
)  =  y )
2 biid 229 . 2  |-  ( x  =  y  <->  x  =  y )
31, 2mpg 1558 1  |-  ( iota
x x  =  y )  =  y
Colors of variables: wff set class
Syntax hints:    <-> wb 178    = wceq 1653   iotacio 5445
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rex 2717  df-v 2964  df-sbc 3168  df-un 3311  df-sn 3844  df-pr 3845  df-uni 4040  df-iota 5447
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