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Theorem nfcvf 2511
 Description: If x and y are distinct, then x is not free in y. (Contributed by Mario Carneiro, 8-Oct-2016.)
Assertion
Ref Expression
nfcvf x x = yxy)

Proof of Theorem nfcvf
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 nfcv 2489 . 2 xz
2 nfcv 2489 . 2 zy
3 id 19 . 2 (z = yz = y)
41, 2, 3dvelimc 2510 1 x x = yxy)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540   = wceq 1642  Ⅎwnfc 2476 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  nfcvf2  2512  nfrald  2665  ralcom2  2775  nfreud  2783  nfrmod  2784  nfrmo  2786  nfiotad  4342
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