Theorem sbcrex 3412

Description: Interchange class substitution and restricted existential quantifier. (Contributed by NM, 15-Nov-2005.) (Revised by NM, 18-Aug-2018.)

Assertion

Ref	Expression
sbcrex

Distinct variable groups:   ,   ,   ,

Proof of Theorem sbcrex

Step	Hyp	Ref	Expression
1		nfcv 2619	. 2
2		sbcrext 3410	. 2
3	1, 2	ax-mp 5	1

Syntax hints:  <->wb 184  F/_wnfc 2605  E.wrex 2808  [.wsbc 3327

This theorem is referenced by:  ac6sfi  7784  csbwrdg  12570  rexfiuz  13180  2sbcrex  30718  sbc2rex  30720

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  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-sbc 3328