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Mirrors > Home > MPE Home > Th. List > ulmf2 | Structured version Unicode version |
Description: Closure of a uniform limit of functions. (Contributed by Mario Carneiro, 18-Mar-2015.) |
Ref | Expression |
---|---|
ulmf2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ulmpm 21964 |
. . . 4
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2 | ovex 6215 |
. . . . . 6
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3 | zex 10756 |
. . . . . 6
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4 | 2, 3 | elpm2 7344 |
. . . . 5
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5 | 4 | simplbi 460 |
. . . 4
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6 | 1, 5 | syl 16 |
. . 3
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7 | 6 | adantl 466 |
. 2
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8 | fndm 5608 |
. . . 4
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9 | 8 | adantr 465 |
. . 3
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10 | 9 | feq2d 5645 |
. 2
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11 | 7, 10 | mpbid 210 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-rep 4501 ax-sep 4511 ax-nul 4519 ax-pow 4568 ax-pr 4629 ax-un 6472 ax-cnex 9439 ax-resscn 9440 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-reu 2802 df-rab 2804 df-v 3070 df-sbc 3285 df-csb 3387 df-dif 3429 df-un 3431 df-in 3433 df-ss 3440 df-nul 3736 df-if 3890 df-pw 3960 df-sn 3976 df-pr 3978 df-op 3982 df-uni 4190 df-iun 4271 df-br 4391 df-opab 4449 df-mpt 4450 df-id 4734 df-xp 4944 df-rel 4945 df-cnv 4946 df-co 4947 df-dm 4948 df-rn 4949 df-res 4950 df-ima 4951 df-iota 5479 df-fun 5518 df-fn 5519 df-f 5520 df-f1 5521 df-fo 5522 df-f1o 5523 df-fv 5524 df-ov 6193 df-oprab 6194 df-mpt2 6195 df-map 7316 df-pm 7317 df-neg 9699 df-z 10748 df-uz 10963 df-ulm 21958 |
This theorem is referenced by: ulmdvlem1 21981 ulmdvlem2 21982 ulmdvlem3 21983 mtestbdd 21986 mbfulm 21987 iblulm 21988 itgulm 21989 itgulm2 21990 lgamgulm2 27156 lgamcvglem 27160 |
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