dfso3 - Mathbox for Scott Fenton

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Theorem dfso3 31601

Description: Expansion of the definition of a strict order. (Contributed by Scott Fenton, 6-Jun-2016.)

**Assertion**
Ref	Expression
dfso3	$/\$ $/\$ $/\$ $\/$ $\/$

**Proof of Theorem dfso3**
Step	Hyp	Ref	Expression
1		ne0i 3921	. . . . 5
2		r19.27zv 4071	. . . . 5 $/\$ $/\$ $/\$ $\/$ $\/$ $/\$ $/\$ $/\$ $\/$ $\/$
3	1, 2	syl 17	. . . 4 $/\$ $/\$ $/\$ $\/$ $\/$ $/\$ $/\$ $/\$ $\/$ $\/$
4	3	ralbiia 2979	. . 3 $/\$ $/\$ $/\$ $\/$ $\/$ $/\$ $/\$ $/\$ $\/$ $\/$
5	4	ralbii 2980	. 2 $/\$ $/\$ $/\$ $\/$ $\/$ $/\$ $/\$ $/\$ $\/$ $\/$
6		df-3an 1039	. . . 4 $/\$ $/\$ $/\$ $\/$ $\/$ $/\$ $/\$ $/\$ $\/$ $\/$
7	6	ralbii 2980	. . 3 $/\$ $/\$ $/\$ $\/$ $\/$ $/\$ $/\$ $/\$ $\/$ $\/$
8	7	2ralbii 2981	. 2 $/\$ $/\$ $/\$ $\/$ $\/$ $/\$ $/\$ $/\$ $\/$ $\/$
9		df-po 5035	. . . 4 $/\$ $/\$
10	9	anbi1i 731	. . 3 $/\$ $\/$ $\/$ $/\$ $/\$ $/\$ $\/$ $\/$
11		df-so 5036	. . 3 $/\$ $\/$ $\/$
12		r19.26-2 3065	. . 3 $/\$ $/\$ $/\$ $\/$ $\/$ $/\$ $/\$ $/\$ $\/$ $\/$
13	10, 11, 12	3bitr4i 292	. 2 $/\$ $/\$ $/\$ $\/$ $\/$
14	5, 8, 13	3bitr4ri 293	1 $/\$ $/\$ $/\$ $\/$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4

wb 196 $/\$ wa 384 $\/$ w3o 1036 $/\$ w3a 1037

wcel 1990

wne 2794

wral 2912

c0 3915 class class class wbr 4653

wpo 5033

wor 5034

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602

This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-v 3202 df-dif 3577 df-nul 3916 df-po 5035 df-so 5036

This theorem is referenced by: (None)