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Theorem nfiota1 6015
 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 6014 . 2 (℩𝑥𝜑) = {𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
2 nfaba1 2909 . . 3 𝑥{𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
32nfuni 4595 . 2 𝑥 {𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
41, 3nfcxfr 2901 1 𝑥(℩𝑥𝜑)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196  ∀wal 1630  {cab 2747  Ⅎwnfc 2890  ∪ cuni 4589  ℩cio 6011 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1989  ax-6 2055  ax-7 2091  ax-9 2149  ax-10 2169  ax-11 2184  ax-12 2197  ax-13 2392  ax-ext 2741 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2048  df-clab 2748  df-cleq 2754  df-clel 2757  df-nfc 2892  df-ral 3056  df-rex 3057  df-sn 4323  df-uni 4590  df-iota 6013 This theorem is referenced by:  iota2df  6037  sniota  6040  opabiota  6425  nfriota1  6783  nfriotad  6784  erovlem  8013  bnj1366  31229  nosupbnd2  32190
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