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Mirrors > Home > ILE Home > Th. List > npsspw | Unicode version |
Description: Lemma for proving existence of reals. (Contributed by Jim Kingdon, 27-Sep-2019.) |
Ref | Expression |
---|---|
npsspw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpll 518 | . . . 4 | |
2 | velpw 3517 | . . . . 5 | |
3 | velpw 3517 | . . . . 5 | |
4 | 2, 3 | anbi12i 455 | . . . 4 |
5 | 1, 4 | sylibr 133 | . . 3 |
6 | 5 | ssopab2i 4199 | . 2 |
7 | df-inp 7274 | . 2 | |
8 | df-xp 4545 | . 2 | |
9 | 6, 7, 8 | 3sstr4i 3138 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 697 w3a 962 wcel 1480 wral 2416 wrex 2417 wss 3071 cpw 3510 class class class wbr 3929 copab 3988 cxp 4537 cnq 7088 cltq 7093 cnp 7099 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-in 3077 df-ss 3084 df-pw 3512 df-opab 3990 df-xp 4545 df-inp 7274 |
This theorem is referenced by: preqlu 7280 npex 7281 elinp 7282 prop 7283 elnp1st2nd 7284 cauappcvgprlemladd 7466 |
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