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Mathbox for Alan Sare |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > csbunigOLD | Structured version Visualization version Unicode version |
Description: Distribute proper substitution through the union of a class. (Contributed by Alan Sare, 10-Nov-2012.) Obsolete as of 22-Aug-2018. Use csbuni 4240 instead. (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
csbunigOLD |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbabgOLD 37251 |
. . 3
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2 | sbcexgOLD 36948 |
. . . . 5
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3 | sbcangOLD 36934 |
. . . . . . 7
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4 | sbcg 3345 |
. . . . . . . 8
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5 | sbcel2gOLD 36950 |
. . . . . . . 8
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6 | 4, 5 | anbi12d 722 |
. . . . . . 7
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7 | 3, 6 | bitrd 261 |
. . . . . 6
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8 | 7 | exbidv 1779 |
. . . . 5
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9 | 2, 8 | bitrd 261 |
. . . 4
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10 | 9 | abbidv 2580 |
. . 3
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11 | 1, 10 | eqtrd 2496 |
. 2
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12 | df-uni 4213 |
. . 3
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13 | 12 | csbeq2i 3794 |
. 2
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14 | df-uni 4213 |
. 2
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15 | 11, 13, 14 | 3eqtr4g 2521 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-v 3059 df-sbc 3280 df-csb 3376 df-uni 4213 |
This theorem is referenced by: csbfv12gALTOLD 37253 csbfv12gALTVD 37336 |
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