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Mirrors > Home > ILE Home > Th. List > ralss | Unicode version |
Description: Restricted universal quantification on a subset in terms of superset. (Contributed by Stefan O'Rear, 3-Apr-2015.) |
Ref | Expression |
---|---|
ralss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3149 |
. . . . 5
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2 | 1 | pm4.71rd 394 |
. . . 4
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3 | 2 | imbi1d 231 |
. . 3
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4 | impexp 263 |
. . 3
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5 | 3, 4 | bitrdi 196 |
. 2
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6 | 5 | ralbidv2 2479 |
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-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-ral 2460 df-in 3135 df-ss 3142 |
This theorem is referenced by: (None) |
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