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Theorem iotajust 4338
Description: Soundness justification theorem for df-iota 4339. (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 3744 . . . . 5
21eqeq2d 2364 . . . 4
32cbvabv 2472 . . 3
4 sneq 3744 . . . . 5
54eqeq2d 2364 . . . 4
65cbvabv 2472 . . 3
73, 6eqtri 2373 . 2
87unieqi 3901 1
Colors of variables: wff setvar class
Syntax hints:   wceq 1642  cab 2339  csn 3737  cuni 3891
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-sn 3741  df-uni 3892
This theorem is referenced by: (None)
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