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Theorem iotajust 5552
 Description: Soundness justification theorem for df-iota 5553. (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 3969 . . . . 5
21eqeq2d 2481 . . . 4
32cbvabv 2595 . . 3
4 sneq 3969 . . . . 5
54eqeq2d 2481 . . . 4
65cbvabv 2595 . . 3
73, 6eqtri 2493 . 2
87unieqi 4199 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1452  cab 2457  csn 3959  cuni 4190 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-rex 2762  df-sn 3960  df-uni 4191 This theorem is referenced by: (None)
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