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Definition df-wetr 4071
 Description: Define the well-ordering predicate. It is unusual to define "well-ordering" in the absence of excluded middle, but we mean an ordering which is like the ordering which we have for ordinals (for example, it does not entail trichotomy because ordinals don't have that as seen at ordtriexmid 4247). Given excluded middle, well-ordering is usually defined to require trichotomy (and the defintion of is typically also different). (Contributed by Mario Carneiro and Jim Kingdon, 23-Sep-2021.)
Assertion
Ref Expression
df-wetr
Distinct variable groups:   ,,,   ,,,

Detailed syntax breakdown of Definition df-wetr
StepHypRef Expression
1 cA . . 3
2 cR . . 3
31, 2wwe 4067 . 2
41, 2wfr 4065 . . 3
5 vx . . . . . . . . . 10
65cv 1242 . . . . . . . . 9
7 vy . . . . . . . . . 10
87cv 1242 . . . . . . . . 9
96, 8, 2wbr 3764 . . . . . . . 8
10 vz . . . . . . . . . 10
1110cv 1242 . . . . . . . . 9
128, 11, 2wbr 3764 . . . . . . . 8
139, 12wa 97 . . . . . . 7
146, 11, 2wbr 3764 . . . . . . 7
1513, 14wi 4 . . . . . 6
1615, 10, 1wral 2306 . . . . 5
1716, 7, 1wral 2306 . . . 4
1817, 5, 1wral 2306 . . 3
194, 18wa 97 . 2
203, 19wb 98 1
 Colors of variables: wff set class This definition is referenced by:  nfwe  4092  weeq1  4093  weeq2  4094  wefr  4095  wepo  4096  wetrep  4097  we0  4098  ordwe  4300  wessep  4302  reg3exmidlemwe  4303
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