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Mirrors > Home > ILE Home > Th. List > cnconst | Unicode version |
Description: A constant function is continuous. (Contributed by FL, 15-Jan-2007.) (Proof shortened by Mario Carneiro, 19-Mar-2015.) |
Ref | Expression |
---|---|
cnconst |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fconst2g 5728 |
. . . 4
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2 | 1 | adantl 277 |
. . 3
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3 | cnconst2 13548 |
. . . . 5
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4 | 3 | 3expa 1203 |
. . . 4
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5 | eleq1 2240 |
. . . 4
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6 | 4, 5 | syl5ibrcom 157 |
. . 3
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7 | 2, 6 | sylbid 150 |
. 2
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8 | 7 | impr 379 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-coll 4116 ax-sep 4119 ax-pow 4172 ax-pr 4207 ax-un 4431 ax-setind 4534 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2739 df-sbc 2963 df-csb 3058 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3809 df-iun 3887 df-br 4002 df-opab 4063 df-mpt 4064 df-id 4291 df-xp 4630 df-rel 4631 df-cnv 4632 df-co 4633 df-dm 4634 df-rn 4635 df-res 4636 df-ima 4637 df-iota 5175 df-fun 5215 df-fn 5216 df-f 5217 df-f1 5218 df-fo 5219 df-f1o 5220 df-fv 5221 df-ov 5873 df-oprab 5874 df-mpo 5875 df-1st 6136 df-2nd 6137 df-map 6645 df-topgen 12695 df-top 13311 df-topon 13324 df-cn 13503 df-cnp 13504 |
This theorem is referenced by: (None) |
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