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Mirrors > Home > ILE Home > Th. List > ovresd | Unicode version |
Description: Lemma for converting metric theorems to metric space theorems. (Contributed by Mario Carneiro, 2-Oct-2015.) |
Ref | Expression |
---|---|
ovresd.1 |
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ovresd.2 |
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Ref | Expression |
---|---|
ovresd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ovresd.1 |
. 2
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2 | ovresd.2 |
. 2
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3 | ovres 6050 |
. 2
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4 | 1, 2, 3 | syl2anc 411 |
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-14 2167 ax-ext 2175 ax-sep 4147 ax-pow 4203 ax-pr 4238 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-ral 2477 df-rex 2478 df-v 2762 df-un 3157 df-in 3159 df-ss 3166 df-pw 3603 df-sn 3624 df-pr 3625 df-op 3627 df-uni 3836 df-br 4030 df-opab 4091 df-xp 4661 df-res 4667 df-iota 5207 df-fv 5254 df-ov 5913 |
This theorem is referenced by: psmetres2 14472 xmetres2 14518 xmssym 14608 xmstri2 14609 mstri2 14610 xmstri 14611 mstri 14612 xmstri3 14613 mstri3 14614 msrtri 14615 limcimolemlt 14789 cnplimcim 14792 cnplimclemr 14794 limccnpcntop 14800 limccnp2lem 14801 |
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