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Theorem nfiota1 6309
Description: Bound-variable hypothesis builder for the class. (Contributed by Andrew Salmon, 11-Jul-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)
Assertion
Ref Expression
nfiota1 𝑥(℩𝑥𝜑)

Proof of Theorem nfiota1
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 dfiota2 6308 . 2 (℩𝑥𝜑) = {𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
2 nfaba1 2983 . . 3 𝑥{𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
32nfuni 4837 . 2 𝑥 {𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
41, 3nfcxfr 2972 1 𝑥(℩𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 207  wal 1526  {cab 2796  wnfc 2958   cuni 4830  cio 6305
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-ral 3140  df-rex 3141  df-sn 4558  df-uni 4831  df-iota 6307
This theorem is referenced by:  iota2df  6335  sniota  6339  opabiota  6739  nfriota1  7110  nfriotadw  7111  nfriotad  7114  erovlem  8382  bnj1366  32000  nosupbnd2  33113
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