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Theorem iotajust 5555
 Description: Soundness justification theorem for df-iota 5556. (Contributed by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
iotajust
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem iotajust
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sneq 4039 . . . . 5
21eqeq2d 2471 . . . 4
32cbvabv 2600 . . 3
4 sneq 4039 . . . . 5
54eqeq2d 2471 . . . 4
65cbvabv 2600 . . 3
73, 6eqtri 2486 . 2
87unieqi 4258 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395  {cab 2442  {csn 4029  U.cuni 4249 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-sn 4030  df-uni 4250
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