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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 | |
ovresd.2 |
Ref | Expression |
---|---|
ovresd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ovresd.1 | . 2 | |
2 | ovresd.2 | . 2 | |
3 | ovres 5961 | . 2 | |
4 | 1, 2, 3 | syl2anc 409 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wcel 2128 cxp 4585 cres 4589 (class class class)co 5825 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-br 3967 df-opab 4027 df-xp 4593 df-res 4599 df-iota 5136 df-fv 5179 df-ov 5828 |
This theorem is referenced by: psmetres2 12775 xmetres2 12821 xmssym 12911 xmstri2 12912 mstri2 12913 xmstri 12914 mstri 12915 xmstri3 12916 mstri3 12917 msrtri 12918 limcimolemlt 13075 cnplimcim 13078 cnplimclemr 13080 limccnpcntop 13086 limccnp2lem 13087 |
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