Theorem rr19.28v 3242

Description: Restricted quantifier version of Theorem 19.28 of [Margaris] p. 90. We don't need the nonempty class condition of r19.28zv 3924 when there is an outer quantifier. (Contributed by NM, 29-Oct-2012.)

Assertion

Ref	Expression
rr19.28v

Distinct variable groups:   ,   ,   ,

Proof of Theorem rr19.28v

Step	Hyp	Ref	Expression
1		simpl 457	. . . . . 6
2	1	ralimi 2850	. . . . 5
3		biidd 237	. . . . . 6
4	3	rspcv 3206	. . . . 5
5	2, 4	syl5 32	. . . 4
6		simpr 461	. . . . . 6
7	6	ralimi 2850	. . . . 5
8	7	a1i 11	. . . 4
9	5, 8	jcad 533	. . 3
10	9	ralimia 2848	. 2
11		r19.28v 2991	. . 3
12	11	ralimi 2850	. 2
13	10, 12	impbii 188	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  e.wcel 1818  A.wral 2807

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