![]() |
Mathbox for Scott Fenton |
< Previous
Next >
Nearby theorems |
|
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 35856 | . 2 ⊢ Bigcup :V–onto→V | |
2 | fofn 6835 | . 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 3482 Fn wfn 6567 –onto→wfo 6570 Bigcup cbigcup 35790 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1793 ax-4 1807 ax-5 1909 ax-6 1967 ax-7 2007 ax-8 2105 ax-9 2113 ax-10 2136 ax-11 2153 ax-12 2173 ax-ext 2705 ax-sep 5320 ax-nul 5327 ax-pow 5386 ax-pr 5450 ax-un 7766 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-3an 1089 df-tru 1540 df-fal 1550 df-ex 1778 df-nf 1782 df-sb 2065 df-mo 2537 df-eu 2566 df-clab 2712 df-cleq 2726 df-clel 2813 df-nfc 2890 df-ne 2943 df-ral 3064 df-rex 3073 df-rab 3439 df-v 3484 df-dif 3973 df-un 3975 df-in 3977 df-ss 3987 df-symdif 4266 df-nul 4348 df-if 4549 df-pw 4624 df-sn 4649 df-pr 4651 df-op 4655 df-uni 4932 df-br 5170 df-opab 5232 df-mpt 5253 df-id 5597 df-eprel 5603 df-xp 5705 df-rel 5706 df-cnv 5707 df-co 5708 df-dm 5709 df-rn 5710 df-res 5711 df-iota 6524 df-fun 6574 df-fn 6575 df-f 6576 df-fo 6578 df-fv 6580 df-1st 8026 df-2nd 8027 df-txp 35810 df-bigcup 35814 |
This theorem is referenced by: fvbigcup 35858 |
Copyright terms: Public domain | W3C validator |