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

Theorem nfald 1852
Description: If is not free in , it is not free in . (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 6-Jan-2018.)
Hypotheses
Ref Expression
nfald.1  F/
nfald.2  F/
Assertion
Ref Expression
nfald  F/

Proof of Theorem nfald
StepHypRef Expression
1 nfald.1 . . 3  F/
2 nfald.2 . . 3  F/
31, 2alrimi 1765 . 2  F/
4 nfnf1 1790 . . . 4  F/ F/
54nfal 1842 . . 3  F/ F/
6 hba1 1786 . . . 4  F/  F/
7 sp 1747 . . . . 5  F/  F/
87nfrd 1763 . . . 4  F/
96, 8hbald 1740 . . 3  F/
105, 9nfd 1766 . 2  F/  F/
113, 10syl 15 1  F/
Colors of variables: wff setvar class
Syntax hints:   wi 4  wal 1540   F/wnf 1544
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
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545
This theorem is referenced by:  nfexd  1854  nfald2  1972  nfsb4t  2080  nfeqd  2503
  Copyright terms: Public domain W3C validator