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Theorem iotajust 5420
 Description: Soundness justification theorem for df-iota 5421. (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 3827 . . . . 5
21eqeq2d 2449 . . . 4
32cbvabv 2557 . . 3
4 sneq 3827 . . . . 5
54eqeq2d 2449 . . . 4
65cbvabv 2557 . . 3
73, 6eqtri 2458 . 2
87unieqi 4027 1
 Colors of variables: wff set class Syntax hints:   wceq 1653  cab 2424  csn 3816  cuni 4017 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-sn 3822  df-uni 4018
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