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Theorem iotaequ 26998
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 6236 . 2  |-  ( A. x ( x  =  y  <->  x  =  y
)  ->  ( iota x x  =  y
)  =  y )
2 biid 229 . 2  |-  ( x  =  y  <->  x  =  y )
31, 2mpg 1542 1  |-  ( iota
x x  =  y )  =  y
Colors of variables: wff set class
Syntax hints:    <-> wb 178    = wceq 1619   iotacio 6223
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2239
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-rex 2524  df-v 2765  df-sbc 2967  df-un 3132  df-sn 3620  df-pr 3621  df-uni 3802  df-iota 6225
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