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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 35864 | . 2 ⊢ Bigcup :V–onto→V | |
2 | fofn 6836 | . 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 3488 Fn wfn 6568 –onto→wfo 6571 Bigcup cbigcup 35798 |
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 2110 ax-9 2118 ax-10 2141 ax-11 2158 ax-12 2178 ax-ext 2711 ax-sep 5317 ax-nul 5324 ax-pow 5383 ax-pr 5447 ax-un 7770 |
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 2543 df-eu 2572 df-clab 2718 df-cleq 2732 df-clel 2819 df-nfc 2895 df-ne 2947 df-ral 3068 df-rex 3077 df-rab 3444 df-v 3490 df-dif 3979 df-un 3981 df-in 3983 df-ss 3993 df-symdif 4272 df-nul 4353 df-if 4549 df-pw 4624 df-sn 4649 df-pr 4651 df-op 4655 df-uni 4932 df-br 5167 df-opab 5229 df-mpt 5250 df-id 5593 df-eprel 5599 df-xp 5706 df-rel 5707 df-cnv 5708 df-co 5709 df-dm 5710 df-rn 5711 df-res 5712 df-iota 6525 df-fun 6575 df-fn 6576 df-f 6577 df-fo 6579 df-fv 6581 df-1st 8030 df-2nd 8031 df-txp 35818 df-bigcup 35822 |
This theorem is referenced by: fvbigcup 35866 |
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