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Mirrors > Home > ILE Home > Th. List > mptfvex | Unicode version |
Description: Sufficient condition for a maps-to notation to be set-like. (Contributed by Mario Carneiro, 3-Jul-2019.) |
Ref | Expression |
---|---|
fvmpt2.1 |
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Ref | Expression |
---|---|
mptfvex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq1 2950 |
. . 3
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2 | fvmpt2.1 |
. . . 4
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3 | nfcv 2235 |
. . . . 5
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4 | nfcsb1v 2977 |
. . . . 5
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5 | csbeq1a 2955 |
. . . . 5
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6 | 3, 4, 5 | cbvmpt 3955 |
. . . 4
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7 | 2, 6 | eqtri 2115 |
. . 3
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8 | 1, 7 | fvmptss2 5414 |
. 2
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9 | elex 2644 |
. . . . . 6
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10 | 9 | alimi 1396 |
. . . . 5
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11 | 3 | nfel1 2246 |
. . . . . 6
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12 | 4 | nfel1 2246 |
. . . . . 6
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13 | 5 | eleq1d 2163 |
. . . . . 6
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14 | 11, 12, 13 | cbval 1691 |
. . . . 5
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15 | 10, 14 | sylib 121 |
. . . 4
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16 | 1 | eleq1d 2163 |
. . . . 5
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17 | 16 | spcgv 2720 |
. . . 4
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18 | 15, 17 | syl5 32 |
. . 3
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19 | 18 | impcom 124 |
. 2
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20 | ssexg 3999 |
. 2
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21 | 8, 19, 20 | sylancr 406 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-14 1457 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 ax-pow 4030 ax-pr 4060 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-rex 2376 df-v 2635 df-sbc 2855 df-csb 2948 df-un 3017 df-in 3019 df-ss 3026 df-pw 3451 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-br 3868 df-opab 3922 df-mpt 3923 df-id 4144 df-xp 4473 df-rel 4474 df-cnv 4475 df-co 4476 df-iota 5014 df-fun 5051 df-fv 5057 |
This theorem is referenced by: mpt2fvex 6011 xpcomco 6622 |
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