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Theorem iotajust 5082
 Description: Soundness justification theorem for df-iota 5083. (Contributed by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
iotajust
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem iotajust
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sneq 3533 . . . . 5
21eqeq2d 2149 . . . 4
32cbvabv 2262 . . 3
4 sneq 3533 . . . . 5
54eqeq2d 2149 . . . 4
65cbvabv 2262 . . 3
73, 6eqtri 2158 . 2
87unieqi 3741 1
 Colors of variables: wff set class Syntax hints:   wceq 1331  cab 2123  csn 3522  cuni 3731 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-sn 3528  df-uni 3732 This theorem is referenced by: (None)
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