Theorem rgen2aOLD 2885

Description: Obsolete proof of rgen2a as of 1-Jan-2020. (Contributed by NM, 23-Nov-1994.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
rgen2a.1

Assertion

Ref	Expression
rgen2aOLD

Distinct variable group:   ,

Proof of Theorem rgen2aOLD

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		eleq1 2529	. . . . . . . 8
2		rgen2a.1	. . . . . . . . 9
3	2	ex 434	. . . . . . . 8
4	1, 3	syl6bi 228	. . . . . . 7
5	4	pm2.43d 48	. . . . . 6
6	5	alimi 1633	. . . . 5
7	6	a1d 25	. . . 4
8		eleq1 2529	. . . . . 6
9	8	dvelimv 2080	. . . . 5
10	3	alimi 1633	. . . . 5
11	9, 10	syl6 33	. . . 4
12	7, 11	pm2.61i 164	. . 3
13		df-ral 2812	. . 3
14	12, 13	sylibr 212	. 2
15	14	rgen 2817	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  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-ex 1613  df-nf 1617  df-cleq 2449  df-clel 2452  df-ral 2812