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Theorem nfiota1 6314
 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 6313 . 2 (℩𝑥𝜑) = {𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
2 nfaba1 2991 . . 3 𝑥{𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
32nfuni 4844 . 2 𝑥 {𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
41, 3nfcxfr 2980 1 𝑥(℩𝑥𝜑)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 207  ∀wal 1528  {cab 2804  Ⅎwnfc 2966  ∪ cuni 4837  ℩cio 6310 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-ral 3148  df-rex 3149  df-sn 4565  df-uni 4838  df-iota 6312 This theorem is referenced by:  iota2df  6340  sniota  6343  opabiota  6743  nfriota1  7113  nfriotadw  7114  nfriotad  7117  erovlem  8383  bnj1366  31987  nosupbnd2  33100
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