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Theorem iotaequ 27597
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 5421 . 2  |-  ( A. x ( x  =  y  <->  x  =  y
)  ->  ( iota x x  =  y
)  =  y )
2 biid 228 . 2  |-  ( x  =  y  <->  x  =  y )
31, 2mpg 1557 1  |-  ( iota
x x  =  y )  =  y
Colors of variables: wff set class
Syntax hints:    <-> wb 177    = wceq 1652   iotacio 5408
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-v 2950  df-sbc 3154  df-un 3317  df-sn 3812  df-pr 3813  df-uni 4008  df-iota 5410
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