New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  sb8 Unicode version

Theorem sb8 2092
 Description: Substitution of variable in universal quantifier. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypothesis
Ref Expression
sb5rf.1
Assertion
Ref Expression
sb8

Proof of Theorem sb8
StepHypRef Expression
1 sb5rf.1 . . . 4
21nfal 1842 . . 3
3 stdpc4 2024 . . 3
42, 3alrimi 1765 . 2
51nfs1 2044 . . 3
6 stdpc7 1917 . . 3
75, 1, 6cbv3 1982 . 2
84, 7impbii 180 1
 Colors of variables: wff setvar class Syntax hints:   wb 176  wal 1540  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:  sb8e  2093  sbhb  2107  sbnf2  2108  sb8eu  2222  sb8iota  4346
 Copyright terms: Public domain W3C validator