Theorem rr19.3v 3241

Description: Restricted quantifier version of Theorem 19.3 of [Margaris] p. 89. We don't need the nonempty class condition of r19.3rzv 3922 when there is an outer quantifier. (Contributed by NM, 25-Oct-2012.)

Assertion

Ref	Expression
rr19.3v

Distinct variable groups:   ,   ,   ,

Proof of Theorem rr19.3v

Step	Hyp	Ref	Expression
1		biidd 237	. . . 4
2	1	rspcv 3206	. . 3
3	2	ralimia 2848	. 2
4		ax-1 6	. . . 4
5	4	ralrimiv 2869	. . 3
6	5	ralimi 2850	. 2
7	3, 6	impbii 188	1

Syntax hints:  <->wb 184  e.wcel 1818  A.wral 2807

This theorem is referenced by:  ispos2  15577

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-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-v 3111