MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfiota1 Structured version   Visualization version   GIF version

Theorem nfiota1 6393
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 6392 . 2 (℩𝑥𝜑) = {𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
2 nfaba1 2915 . . 3 𝑥{𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
32nfuni 4846 . 2 𝑥 {𝑦 ∣ ∀𝑥(𝜑𝑥 = 𝑦)}
41, 3nfcxfr 2905 1 𝑥(℩𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wal 1537  {cab 2715  wnfc 2887   cuni 4839  cio 6389
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-ex 1783  df-nf 1787  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-nfc 2889  df-ral 3069  df-rex 3070  df-v 3434  df-in 3894  df-ss 3904  df-sn 4562  df-uni 4840  df-iota 6391
This theorem is referenced by:  iota2df  6420  sniota  6424  opabiota  6851  nfriota1  7239  nfriotadw  7240  nfriotad  7244  erovlem  8602  bnj1366  32809  nosupbnd2  33919  noinfbnd2  33934
  Copyright terms: Public domain W3C validator