Theorem mo3OLD 2324

Description: Obsolete proof of mo3 2323 as of 20-Jul-2019. (Contributed by NM, 8-Mar-1995.) (Revised by Wolf Lammen, 3-Dec-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
mo3.1

Assertion

Ref	Expression
mo3OLD

Distinct variable group:   ,

Proof of Theorem mo3OLD

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		mo2v 2289	. . 3
2		mo3.1	. . . . . . . . 9
3		nfv 1707	. . . . . . . . 9
4	2, 3	nfim 1920	. . . . . . . 8
5		nfs1v 2181	. . . . . . . . 9
6		nfv 1707	. . . . . . . . 9
7	5, 6	nfim 1920	. . . . . . . 8
8		sbequ2 1741	. . . . . . . . 9
9		ax-7 1790	. . . . . . . . 9
10	8, 9	imim12d 74	. . . . . . . 8
11	4, 7, 10	cbv3 2015	. . . . . . 7
12	11	ancli 551	. . . . . 6
13	4, 7	aaan 1975	. . . . . 6
14	12, 13	sylibr 212	. . . . 5
15		prth 571	. . . . . . 7
16		equtr2 1802	. . . . . . 7
17	15, 16	syl6 33	. . . . . 6
18	17	2alimi 1634	. . . . 5
19	14, 18	syl 16	. . . 4
20	19	exlimiv 1722	. . 3
21	1, 20	sylbi 195	. 2
22		nfa1 1897	. . . . . 6
23		pm3.3 444	. . . . . . . . . 10
24	23	com3r 79	. . . . . . . . 9
25	5, 24	alimd 1876	. . . . . . . 8
26	25	com12 31	. . . . . . 7
27	26	sps 1865	. . . . . 6
28	22, 27	eximd 1882	. . . . 5
29	2	sb8e 2168	. . . . 5
30	2	mo2 2293	. . . . 5
31	28, 29, 30	3imtr4g 270	. . . 4
32		moabs 2315	. . . 4
33	31, 32	sylibr 212	. . 3
34	33	alcoms 1843	. 2
35	21, 34	impbii 188	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  F/wnf 1616  [wsb 1739  E*wmo 2283

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

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287