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Axiom ax-pre-sup 9099
 Description: A non-empty, bounded-above set of reals has a supremum. Axiom 22 of 22 for real and complex numbers, justified by theorem axpre-sup 9075. Note: Normally new proofs would use axsup 9182. (New usage is discouraged.) (Contributed by NM, 13-Oct-2005.)
Assertion
Ref Expression
ax-pre-sup
Distinct variable group:   ,,,

Detailed syntax breakdown of Axiom ax-pre-sup
StepHypRef Expression
1 cA . . . 4
2 cr 9020 . . . 4
31, 2wss 3306 . . 3
4 c0 3613 . . . 4
51, 4wne 2605 . . 3
6 vy . . . . . . 7
76cv 1652 . . . . . 6
8 vx . . . . . . 7
98cv 1652 . . . . . 6
10 cltrr 9025 . . . . . 6
117, 9, 10wbr 4237 . . . . 5
1211, 6, 1wral 2711 . . . 4
1312, 8, 2wrex 2712 . . 3
143, 5, 13w3a 937 . 2
159, 7, 10wbr 4237 . . . . . 6
1615wn 3 . . . . 5
1716, 6, 1wral 2711 . . . 4
18 vz . . . . . . . . 9
1918cv 1652 . . . . . . . 8
207, 19, 10wbr 4237 . . . . . . 7
2120, 18, 1wrex 2712 . . . . . 6
2211, 21wi 4 . . . . 5
2322, 6, 2wral 2711 . . . 4
2417, 23wa 360 . . 3
2524, 8, 2wrex 2712 . 2
2614, 25wi 4 1
 Colors of variables: wff set class This axiom is referenced by:  axsup  9182
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