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

Step	Hyp	Ref	Expression
1		sb5rf.1	. 2
2	1	nfs1 2104	. 2
3		sbequ12 1992	. 2
4	1, 2, 3	cbvex 2022	1

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