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Axiom ax-ddkcomp 13176
 Description: Axiom of Dedekind completeness for Dedekind real numbers: every inhabited upper-bounded located set of reals has a real upper bound. Ideally, this axiom should be "proved" as "axddkcomp" for the real numbers constructed from IZF, and then the axiom ax-ddkcomp 13176 should be used in place of construction specific results. In particular, axcaucvg 7701 should be proved from it. (Contributed by BJ, 24-Oct-2021.)
Assertion
Ref Expression
ax-ddkcomp

Detailed syntax breakdown of Axiom ax-ddkcomp
StepHypRef Expression
1 cA . . . . 5
2 cr 7612 . . . . 5
31, 2wss 3066 . . . 4
4 vx . . . . . . 7
54cv 1330 . . . . . 6
65, 1wcel 1480 . . . . 5
76, 4wex 1468 . . . 4
83, 7wa 103 . . 3
9 vy . . . . . . 7
109cv 1330 . . . . . 6
11 clt 7793 . . . . . 6
1210, 5, 11wbr 3924 . . . . 5
1312, 9, 1wral 2414 . . . 4
1413, 4, 2wrex 2415 . . 3
155, 10, 11wbr 3924 . . . . . 6
16 vz . . . . . . . . . 10
1716cv 1330 . . . . . . . . 9
185, 17, 11wbr 3924 . . . . . . . 8
1918, 16, 1wrex 2415 . . . . . . 7
2017, 10, 11wbr 3924 . . . . . . . 8
2120, 16, 1wral 2414 . . . . . . 7
2219, 21wo 697 . . . . . 6
2315, 22wi 4 . . . . 5
2423, 9, 2wral 2414 . . . 4
2524, 4, 2wral 2414 . . 3
268, 14, 25w3a 962 . 2
27 cle 7794 . . . . . 6
2810, 5, 27wbr 3924 . . . . 5
2928, 9, 1wral 2414 . . . 4
30 cB . . . . . . 7
31 cR . . . . . . 7
3230, 31wcel 1480 . . . . . 6
3310, 30, 27wbr 3924 . . . . . . 7
3433, 9, 1wral 2414 . . . . . 6
3532, 34wa 103 . . . . 5
365, 30, 27wbr 3924 . . . . 5
3735, 36wi 4 . . . 4
3829, 37wa 103 . . 3
3938, 4, 2wrex 2415 . 2
4026, 39wi 4 1
 Colors of variables: wff set class This axiom is referenced by: (None)
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