Theorem mob2 3279

Description: Consequence of "at most one." (Contributed by NM, 2-Jan-2015.)

Hypothesis

Ref	Expression
moi2.1

Assertion

Ref	Expression
mob2

Distinct variable groups:   ,   ,

Proof of Theorem mob2

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		simp3 998	. . 3
2		moi2.1	. . 3
3	1, 2	syl5ibcom 220	. 2
4		nfs1v 2181	. . . . . . . 8
5		sbequ12 1992	. . . . . . . 8
6	4, 5	mo4f 2336	. . . . . . 7
7		sp 1859	. . . . . . 7
8	6, 7	sylbi 195	. . . . . 6
9		nfv 1707	. . . . . . . . . 10
10	9, 2	sbhypf 3156	. . . . . . . . 9
11	10	anbi2d 703	. . . . . . . 8
12		eqeq2 2472	. . . . . . . 8
13	11, 12	imbi12d 320	. . . . . . 7
14	13	spcgv 3194	. . . . . 6
15	8, 14	syl5 32	. . . . 5
16	15	imp 429	. . . 4
17	16	expd 436	. . 3
18	17	3impia 1193	. 2
19	3, 18	impbid 191	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  A.wal 1393  =wceq 1395  [wsb 1739  e.wcel 1818  E*wmo 2283

This theorem is referenced by:  moi2  3280  mob  3281  rmob2  3432

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-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111