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Mirrors > Home > MPE Home > Th. List > ssres2 | Structured version Visualization version Unicode version |
Description: Subclass theorem for restriction. (Contributed by NM, 22-Mar-1998.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
ssres2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpss1 4943 |
. . 3
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2 | sslin 3658 |
. . 3
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3 | 1, 2 | syl 17 |
. 2
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4 | df-res 4846 |
. 2
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5 | df-res 4846 |
. 2
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6 | 3, 4, 5 | 3sstr4g 3473 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-v 3047 df-in 3411 df-ss 3418 df-opab 4462 df-xp 4840 df-res 4846 |
This theorem is referenced by: imass2 5204 1stcof 6821 2ndcof 6822 tfrlem15 7110 gsum2dlem2 17603 txkgen 20667 funpsstri 30406 resnonrel 36198 mptrcllem 36220 rtrclexi 36228 cnvrcl0 36232 relexpss1d 36297 relexp0a 36308 |
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