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Axiom ax-pre-sup 9591
Description: A nonempty, bounded-above set of reals has a supremum. Axiom 22 of 22 for real and complex numbers, justified by theorem axpre-sup 9567. Note: Normally new proofs would use axsup 9681. (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 9512 . . . 4
31, 2wss 3475 . . 3
4 c0 3784 . . . 4
51, 4wne 2652 . . 3
6 vy . . . . . . 7
76cv 1394 . . . . . 6
8 vx . . . . . . 7
98cv 1394 . . . . . 6
10 cltrr 9517 . . . . . 6
117, 9, 10wbr 4452 . . . . 5
1211, 6, 1wral 2807 . . . 4
1312, 8, 2wrex 2808 . . 3
143, 5, 13w3a 973 . 2
159, 7, 10wbr 4452 . . . . . 6
1615wn 3 . . . . 5
1716, 6, 1wral 2807 . . . 4
18 vz . . . . . . . . 9
1918cv 1394 . . . . . . . 8
207, 19, 10wbr 4452 . . . . . . 7
2120, 18, 1wrex 2808 . . . . . 6
2211, 21wi 4 . . . . 5
2322, 6, 2wral 2807 . . . 4
2417, 23wa 369 . . 3
2524, 8, 2wrex 2808 . 2
2614, 25wi 4 1
Colors of variables: wff setvar class
This axiom is referenced by:  axsup  9681
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