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Mirrors > Home > MPE Home > Th. List > Mathboxes > fnbigcup | Structured version Visualization version GIF version |
Description: Bigcup is a function over the universal class. (Contributed by Scott Fenton, 11-Apr-2012.) |
Ref | Expression |
---|---|
fnbigcup | ⊢ Bigcup Fn V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fobigcup 33354 | . 2 ⊢ Bigcup :V–onto→V | |
2 | fofn 6585 | . 2 ⊢ ( Bigcup :V–onto→V → Bigcup Fn V) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ Bigcup Fn V |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3493 Fn wfn 6343 –onto→wfo 6346 Bigcup cbigcup 33288 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1905 ax-6 1964 ax-7 2009 ax-8 2110 ax-9 2118 ax-10 2139 ax-11 2154 ax-12 2170 ax-ext 2791 ax-sep 5194 ax-nul 5201 ax-pow 5257 ax-pr 5320 ax-un 7453 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1084 df-tru 1534 df-ex 1775 df-nf 1779 df-sb 2064 df-mo 2616 df-eu 2648 df-clab 2798 df-cleq 2812 df-clel 2891 df-nfc 2961 df-ne 3015 df-ral 3141 df-rex 3142 df-rab 3145 df-v 3495 df-sbc 3771 df-dif 3937 df-un 3939 df-in 3941 df-ss 3950 df-symdif 4217 df-nul 4290 df-if 4466 df-pw 4539 df-sn 4560 df-pr 4562 df-op 4566 df-uni 4831 df-br 5058 df-opab 5120 df-mpt 5138 df-id 5453 df-eprel 5458 df-xp 5554 df-rel 5555 df-cnv 5556 df-co 5557 df-dm 5558 df-rn 5559 df-res 5560 df-iota 6307 df-fun 6350 df-fn 6351 df-f 6352 df-fo 6354 df-fv 6356 df-1st 7681 df-2nd 7682 df-txp 33308 df-bigcup 33312 |
This theorem is referenced by: fvbigcup 33356 |
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