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Mirrors > Home > ILE Home > Th. List > csbresg | Unicode version |
Description: Distribute proper substitution through the restriction of a class. (Contributed by Alan Sare, 10-Nov-2012.) |
Ref | Expression |
---|---|
csbresg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbing 3342 |
. . 3
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2 | csbxpg 4707 |
. . . . 5
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3 | csbconstg 3071 |
. . . . . 6
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4 | 3 | xpeq2d 4650 |
. . . . 5
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5 | 2, 4 | eqtrd 2210 |
. . . 4
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6 | 5 | ineq2d 3336 |
. . 3
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7 | 1, 6 | eqtrd 2210 |
. 2
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8 | df-res 4638 |
. . 3
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9 | 8 | csbeq2i 3084 |
. 2
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10 | df-res 4638 |
. 2
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11 | 7, 9, 10 | 3eqtr4g 2235 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 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-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rab 2464 df-v 2739 df-sbc 2963 df-csb 3058 df-in 3135 df-opab 4065 df-xp 4632 df-res 4638 |
This theorem is referenced by: (None) |
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