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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 2908 . . 3 𝑥{𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
32nfuni 4813 . 2 𝑥 {𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
41, 3nfcxfr 2898 1 𝑥(℩𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 209  wal 1540  {cab 2717  wnfc 2880   cuni 4806  cio 6305
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2162  ax-12 2179  ax-ext 2711
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-tru 1545  df-ex 1787  df-nf 1791  df-sb 2075  df-clab 2718  df-cleq 2731  df-clel 2812  df-nfc 2882  df-ral 3059  df-rex 3060  df-v 3402  df-in 3860  df-ss 3870  df-sn 4527  df-uni 4807  df-iota 6307
This theorem is referenced by:  iota2df  6336  sniota  6340  opabiota  6763  nfriota1  7146  nfriotadw  7147  nfriotad  7151  erovlem  8436  bnj1366  32392  nosupbnd2  33574  noinfbnd2  33589
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