NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  nfs1 Unicode version

Theorem nfs1 2044
Description: If is not free in , is not free in . (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfs1.1  F/
Assertion
Ref Expression
nfs1  F/

Proof of Theorem nfs1
StepHypRef Expression
1 nfs1.1 . . . 4  F/
21nfri 1762 . . 3
32hbsb3 2043 . 2
43nfi 1551 1  F/
Colors of variables: wff setvar class
Syntax hints:   F/wnf 1544  wsb 1648
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
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649
This theorem is referenced by:  ax16ALT2  2048  sbco2  2086  sb8  2092  mo  2226  ralxpf  4827
  Copyright terms: Public domain W3C validator