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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpll 527 |
. . . 4
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2 | velpw 3600 |
. . . . 5
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3 | velpw 3600 |
. . . . 5
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4 | 2, 3 | anbi12i 460 |
. . . 4
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5 | 1, 4 | sylibr 134 |
. . 3
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6 | 5 | ssopab2i 4298 |
. 2
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7 | df-inp 7500 |
. 2
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8 | df-xp 4653 |
. 2
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9 | 6, 7, 8 | 3sstr4i 3211 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-in 3150 df-ss 3157 df-pw 3595 df-opab 4083 df-xp 4653 df-inp 7500 |
This theorem is referenced by: preqlu 7506 npex 7507 elinp 7508 prop 7509 elnp1st2nd 7510 cauappcvgprlemladd 7692 |
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