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Mirrors > Home > ILE Home > Th. List > fvunsng | Unicode version |
Description: Remove an ordered pair not participating in a function value. (Contributed by Jim Kingdon, 7-Jan-2019.) |
Ref | Expression |
---|---|
fvunsng |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snidg 3447 |
. . . 4
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2 | fvres 5274 |
. . . 4
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3 | 1, 2 | syl 14 |
. . 3
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4 | resundir 4685 |
. . . . 5
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5 | elsni 3440 |
. . . . . . . . 9
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6 | 5 | necon3ai 2298 |
. . . . . . . 8
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7 | ressnop0 5420 |
. . . . . . . 8
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8 | 6, 7 | syl 14 |
. . . . . . 7
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9 | 8 | uneq2d 3138 |
. . . . . 6
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10 | un0 3299 |
. . . . . 6
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11 | 9, 10 | syl6eq 2131 |
. . . . 5
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12 | 4, 11 | syl5eq 2127 |
. . . 4
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13 | 12 | fveq1d 5255 |
. . 3
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14 | 3, 13 | sylan9req 2136 |
. 2
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15 | fvres 5274 |
. . . 4
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16 | 1, 15 | syl 14 |
. . 3
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17 | 16 | adantr 270 |
. 2
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18 | 14, 17 | eqtrd 2115 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-14 1446 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-sep 3922 ax-pow 3974 ax-pr 4000 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-fal 1291 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ne 2250 df-ral 2358 df-rex 2359 df-v 2614 df-dif 2986 df-un 2988 df-in 2990 df-ss 2997 df-nul 3270 df-pw 3408 df-sn 3428 df-pr 3429 df-op 3431 df-uni 3628 df-br 3812 df-opab 3866 df-xp 4407 df-res 4413 df-iota 4934 df-fv 4977 |
This theorem is referenced by: fvpr1 5441 fvpr1g 5443 fvpr2g 5444 fvtp1g 5445 tfrlemisucaccv 6022 tfr1onlemsucaccv 6038 tfrcllemsucaccv 6051 ac6sfi 6544 0tonninf 9734 1tonninf 9735 hashennn 10023 |
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