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Theorem iotaequ 27497
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 5388 . 2  |-  ( A. x ( x  =  y  <->  x  =  y
)  ->  ( iota x x  =  y
)  =  y )
2 biid 228 . 2  |-  ( x  =  y  <->  x  =  y )
31, 2mpg 1554 1  |-  ( iota
x x  =  y )  =  y
Colors of variables: wff set class
Syntax hints:    <-> wb 177    = wceq 1649   iotacio 5375
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rex 2672  df-v 2918  df-sbc 3122  df-un 3285  df-sn 3780  df-pr 3781  df-uni 3976  df-iota 5377
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