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Mirrors > Home > MPE Home > Th. List > fvpr2 | Structured version Visualization version Unicode version |
Description: The value of a function with a domain of two elements. (Contributed by Jeff Madsen, 20-Jun-2010.) |
Ref | Expression |
---|---|
fvpr2.1 |
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fvpr2.2 |
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Ref | Expression |
---|---|
fvpr2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prcom 4041 |
. . 3
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2 | 1 | fveq1i 5880 |
. 2
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3 | necom 2696 |
. . 3
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4 | fvpr2.1 |
. . . 4
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5 | fvpr2.2 |
. . . 4
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6 | 4, 5 | fvpr1 6123 |
. . 3
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7 | 3, 6 | sylbi 200 |
. 2
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8 | 2, 7 | syl5eq 2517 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-8 1906 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-sep 4518 ax-nul 4527 ax-pow 4579 ax-pr 4639 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-sbc 3256 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-br 4396 df-opab 4455 df-id 4754 df-xp 4845 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-res 4851 df-iota 5553 df-fun 5591 df-fv 5597 |
This theorem is referenced by: fnprb 6139 m2detleiblem3 19731 m2detleiblem4 19732 axlowdimlem6 25056 wlkntrllem2 25369 wlkntrllem3 25370 2wlklem1 25406 ex-fv 25972 fprb 30484 nnsum3primes4 39028 nnsum3primesgbe 39032 umgr2v2evd2 39750 zlmodzxzldeplem3 40803 |
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