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Mirrors > Home > MPE Home > Th. List > atandm | Structured version Visualization version Unicode version |
Description: Since the property is a
little lengthy, we abbreviate
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Ref | Expression |
---|---|
atandm |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldif 3426 |
. . 3
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2 | elprg 3996 |
. . . . . 6
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3 | 2 | notbid 300 |
. . . . 5
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4 | neanior 2728 |
. . . . 5
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5 | 3, 4 | syl6bbr 271 |
. . . 4
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6 | 5 | pm5.32i 647 |
. . 3
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7 | 1, 6 | bitri 257 |
. 2
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8 | ovex 6343 |
. . . 4
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9 | df-atan 23842 |
. . . 4
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10 | 8, 9 | dmmpti 5729 |
. . 3
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11 | 10 | eleq2i 2532 |
. 2
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12 | 3anass 995 |
. 2
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13 | 7, 11, 12 | 3bitr4i 285 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4539 ax-nul 4548 ax-pr 4653 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-rab 2758 df-v 3059 df-sbc 3280 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4213 df-br 4417 df-opab 4476 df-mpt 4477 df-id 4768 df-xp 4859 df-rel 4860 df-cnv 4861 df-co 4862 df-dm 4863 df-iota 5565 df-fun 5603 df-fn 5604 df-fv 5609 df-ov 6318 df-atan 23842 |
This theorem is referenced by: atandm2 23852 atandm3 23853 atancj 23885 2efiatan 23893 tanatan 23894 dvatan 23910 |
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