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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1 3608 | . . . 4 | |
2 | 1 | unieqd 3755 | . . 3 |
3 | uneq1 3228 | . . 3 | |
4 | 2, 3 | eqeq12d 2155 | . 2 |
5 | preq2 3609 | . . . 4 | |
6 | 5 | unieqd 3755 | . . 3 |
7 | uneq2 3229 | . . 3 | |
8 | 6, 7 | eqeq12d 2155 | . 2 |
9 | vex 2692 | . . 3 | |
10 | vex 2692 | . . 3 | |
11 | 9, 10 | unipr 3758 | . 2 |
12 | 4, 8, 11 | vtocl2g 2753 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1332 wcel 1481 cun 3074 cpr 3533 cuni 3744 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-uni 3745 |
This theorem is referenced by: onun2 4414 unopn 12211 |
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