Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfcvf2 GIF version

Theorem nfcvf2 2242
 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 2241 . 2 (¬ ∀𝑦 𝑦 = 𝑥𝑦𝑥)
21naecoms 1653 1 (¬ ∀𝑥 𝑥 = 𝑦𝑦𝑥)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1283  Ⅎwnfc 2207 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291  df-nf 1391  df-sb 1687  df-cleq 2075  df-clel 2078  df-nfc 2209 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator