Theorem mo2 2293

Description: Alternate definition of "at most one." (Contributed by NM, 8-Mar-1995.) Restrict dummy variable z. (Revised by Wolf Lammen, 28-May-2019.)

Hypothesis

Ref	Expression
mo2.1

Assertion

Ref	Expression
mo2

Distinct variable group:   ,

Proof of Theorem mo2

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		mo2v 2289	. 2
2		mo2.1	. . . . 5
3		nfv 1707	. . . . 5
4	2, 3	nfim 1920	. . . 4
5	4	nfal 1947	. . 3
6		nfv 1707	. . 3
7		equequ2 1799	. . . . 5
8	7	imbi2d 316	. . . 4
9	8	albidv 1713	. . 3
10	5, 6, 9	cbvex 2022	. 2
11	1, 10	bitri 249	1

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

This theorem is referenced by:  mo3  2323  mo3OLD  2324  mo  2325  eu5OLD  2330  morimvOLD  2342  rmo2  3427  nmo  27384  bj-eu3f  34413

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-eu 2286  df-mo 2287