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Mirrors > Home > ILE Home > Th. List > uniprg | Unicode version |
Description: The union of a pair is the union of its members. Proposition 5.7 of [TakeutiZaring] p. 16. (Contributed by NM, 25-Aug-2006.) |
Ref | Expression |
---|---|
uniprg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1 3447 |
. . . 4
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2 | 1 | unieqd 3591 |
. . 3
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3 | uneq1 3090 |
. . 3
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4 | 2, 3 | eqeq12d 2054 |
. 2
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5 | preq2 3448 |
. . . 4
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6 | 5 | unieqd 3591 |
. . 3
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7 | uneq2 3091 |
. . 3
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8 | 6, 7 | eqeq12d 2054 |
. 2
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9 | vex 2560 |
. . 3
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10 | vex 2560 |
. . 3
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11 | 9, 10 | unipr 3594 |
. 2
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12 | 4, 8, 11 | vtocl2g 2617 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-uni 3581 |
This theorem is referenced by: onun2 4216 |
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