Theorem rspesbca 3419

Description: Existence form of rspsbca 3418. (Contributed by NM, 29-Feb-2008.) (Proof shortened by Mario Carneiro, 13-Oct-2016.)

Assertion

Ref	Expression
rspesbca

Distinct variable group:   ,

Proof of Theorem rspesbca

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfsbcq2 3330	. . 3
2	1	rspcev 3210	. 2
3		cbvrexsv 3096	. 2
4	2, 3	sylibr 212	1

Syntax hints:  ->wi 4  /\wa 369  [wsb 1739  e.wcel 1818  E.wrex 2808  [.wsbc 3327

This theorem is referenced by:  spesbc  3420  indexfi  7848  indexdom  30225

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-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