MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  sb8e Unicode version

Theorem sb8e 2168
Description: Substitution of variable in existential quantifier. (Contributed by NM, 12-Aug-1993.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Jim Kingdon, 15-Jan-2018.)
Hypothesis
Ref Expression
sb5rf.1
Assertion
Ref Expression
sb8e

Proof of Theorem sb8e
StepHypRef Expression
1 sb5rf.1 . 2
21nfs1 2104 . 2
3 sbequ12 1992 . 2
41, 2, 3cbvex 2022 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  E.wex 1612  F/wnf 1616  [wsb 1739
This theorem is referenced by:  sbnf2  2183  2sb8e  2211  sb8mo  2320  mo3  2323  mo3OLD  2324  mopickOLD  2357  sbcexf  30518  exlimddvfi  30527  pm11.58  31296  bnj985  34011
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
  Copyright terms: Public domain W3C validator