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Mirrors > Home > MPE Home > Th. List > iunex | Unicode version |
Description: The existence of an
indexed union. is normally a free-variable
parameter in the class expression substituted for , which can be
read informally as ( x ) . (Contributed by NM,
13-Oct-2003.) |
Ref | Expression |
---|---|
iunex.1 | |
iunex.2 |
Ref | Expression |
---|---|
iunex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iunex.1 | . 2 | |
2 | iunex.2 | . . 3 | |
3 | 2 | rgenw 2818 | . 2 |
4 | iunexg 6776 | . 2 | |
5 | 1, 3, 4 | mp2an 672 | 1 |
Colors of variables: wff setvar class |
Syntax hints: e. wcel 1818 A. wral 2807
cvv 3109
U_ ciun 4330 |
This theorem is referenced by: abrexex2 6781 tz9.1 8181 tz9.1c 8182 cplem2 8329 fseqdom 8428 pwsdompw 8605 cfsmolem 8671 ac6c4 8882 konigthlem 8964 alephreg 8978 pwfseqlem4 9061 pwfseqlem5 9062 pwxpndom2 9064 wunex2 9137 wuncval2 9146 inar1 9174 isfunc 15233 dfac14 20119 txcmplem2 20143 cnextfval 20562 dfrtrclrec2 29066 rtrclreclem.refl 29067 rtrclreclem.subset 29068 rtrclreclem.min 29070 colinearex 29710 volsupnfl 30059 heiborlem3 30309 bnj893 33986 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 ax-8 1820 ax-9 1822 ax-10 1837 ax-11 1842 ax-12 1854 ax-13 1999 ax-ext 2435 ax-rep 4563 ax-sep 4573 ax-nul 4581 ax-pr 4691 ax-un 6592 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 975 df-tru 1398 df-ex 1613 df-nf 1617 df-sb 1740 df-eu 2286 df-mo 2287 df-clab 2443 df-cleq 2449 df-clel 2452 df-nfc 2607 df-ne 2654 df-ral 2812 df-rex 2813 df-reu 2814 df-rab 2816 df-v 3111 df-sbc 3328 df-csb 3435 df-dif 3478 df-un 3480 df-in 3482 df-ss 3489 df-nul 3785 df-if 3942 df-sn 4030 df-pr 4032 df-op 4036 df-uni 4250 df-iun 4332 df-br 4453 df-opab 4511 df-mpt 4512 df-id 4800 df-xp 5010 df-rel 5011 df-cnv 5012 df-co 5013 df-dm 5014 df-rn 5015 df-res 5016 df-ima 5017 df-iota 5556 df-fun 5595 df-fn 5596 df-f 5597 df-f1 5598 df-fo 5599 df-f1o 5600 df-fv 5601 |
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