NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  nfcvf2 GIF version

Theorem nfcvf2 2512
Description: If x and y are distinct, then y is not free in x. (Contributed by Mario Carneiro, 5-Dec-2016.)
Assertion
Ref Expression
nfcvf2 x x = yyx)

Proof of Theorem nfcvf2
StepHypRef Expression
1 nfcvf 2511 . 2 y y = xyx)
21naecoms 1948 1 x x = yyx)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1540  wnfc 2476
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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478
This theorem is referenced by:  dfid3  4768  oprabid  5550
  Copyright terms: Public domain W3C validator