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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 34417 | . 2 ⊢ Bigcup :V–onto→V | |
2 | fofn 6756 | . 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 3444 Fn wfn 6489 –onto→wfo 6492 Bigcup cbigcup 34351 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2709 ax-sep 5255 ax-nul 5262 ax-pow 5319 ax-pr 5383 ax-un 7665 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2540 df-eu 2569 df-clab 2716 df-cleq 2730 df-clel 2816 df-nfc 2888 df-ne 2943 df-ral 3064 df-rex 3073 df-rab 3407 df-v 3446 df-dif 3912 df-un 3914 df-in 3916 df-ss 3926 df-symdif 4201 df-nul 4282 df-if 4486 df-pw 4561 df-sn 4586 df-pr 4588 df-op 4592 df-uni 4865 df-br 5105 df-opab 5167 df-mpt 5188 df-id 5530 df-eprel 5536 df-xp 5638 df-rel 5639 df-cnv 5640 df-co 5641 df-dm 5642 df-rn 5643 df-res 5644 df-iota 6446 df-fun 6496 df-fn 6497 df-f 6498 df-fo 6500 df-fv 6502 df-1st 7914 df-2nd 7915 df-txp 34371 df-bigcup 34375 |
This theorem is referenced by: fvbigcup 34419 |
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