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Mirrors > Home > MPE Home > Th. List > uniprg | Structured version Visualization version 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 4268 | . . . 4 | |
2 | 1 | unieqd 4446 | . . 3 |
3 | uneq1 3760 | . . 3 | |
4 | 2, 3 | eqeq12d 2637 | . 2 |
5 | preq2 4269 | . . . 4 | |
6 | 5 | unieqd 4446 | . . 3 |
7 | uneq2 3761 | . . 3 | |
8 | 6, 7 | eqeq12d 2637 | . 2 |
9 | vex 3203 | . . 3 | |
10 | vex 3203 | . . 3 | |
11 | 9, 10 | unipr 4449 | . 2 |
12 | 4, 8, 11 | vtocl2g 3270 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cun 3572 cpr 4179 cuni 4436 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-v 3202 df-un 3579 df-sn 4178 df-pr 4180 df-uni 4437 |
This theorem is referenced by: wunun 9532 tskun 9608 gruun 9628 mrcun 16282 unopn 20708 indistopon 20805 unconn 21232 limcun 23659 sshjval3 28213 prsiga 30194 unelsiga 30197 unelldsys 30221 measxun2 30273 measssd 30278 carsgsigalem 30377 carsgclctun 30383 pmeasmono 30386 probun 30481 indispconn 31216 kelac2 37635 fourierdlem70 40393 fourierdlem71 40394 saluncl 40537 prsal 40538 meadjun 40679 omeunle 40730 |
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