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Mirrors > Home > MPE Home > Th. List > imauni | Unicode version |
Description: The image of a union is the indexed union of the images. Theorem 3K(a) of [Enderton] p. 50. (Contributed by NM, 9-Aug-2004.) (Proof shortened by Mario Carneiro, 18-Jun-2014.) |
Ref | Expression |
---|---|
imauni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uniiun 4383 | . . 3 | |
2 | 1 | imaeq2i 5340 | . 2 |
3 | imaiun 6157 | . 2 | |
4 | 2, 3 | eqtri 2486 | 1 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1395 U. cuni 4249
U_ ciun 4330 " cima 5007 |
This theorem is referenced by: enfin2i 8722 tgcn 19753 cncmp 19892 qtoptop2 20200 mbfimaopnlem 22062 |
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-9 1822 ax-10 1837 ax-11 1842 ax-12 1854 ax-13 1999 ax-ext 2435 ax-sep 4573 ax-nul 4581 ax-pr 4691 |
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-rab 2816 df-v 3111 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-xp 5010 df-cnv 5012 df-dm 5014 df-rn 5015 df-res 5016 df-ima 5017 |
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