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Theorem nfiota1 4341
 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 4340 . 2 (℩xφ) = {y x(φx = y)}
2 nfaba1 2494 . . 3 x{y x(φx = y)}
32nfuni 3897 . 2 x{y x(φx = y)}
41, 3nfcxfr 2486 1 x(℩xφ)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176  ∀wal 1540   = wceq 1642  {cab 2339  Ⅎwnfc 2476  ∪cuni 3891  ℩cio 4337 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-sn 3741  df-uni 3892  df-iota 4339 This theorem is referenced by:  iota2df  4365  sniota  4369
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