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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-inf2vnlem3 | Unicode version |
Description: Lemma for bj-inf2vn 14729. (Contributed by BJ, 8-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-inf2vnlem3.bd1 |
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bj-inf2vnlem3.bd2 |
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Ref | Expression |
---|---|
bj-inf2vnlem3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-inf2vnlem2 14726 |
. . 3
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2 | bj-inf2vnlem3.bd1 |
. . . . . 6
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3 | 2 | bdeli 14601 |
. . . . 5
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4 | bj-inf2vnlem3.bd2 |
. . . . . 6
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5 | 4 | bdeli 14601 |
. . . . 5
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6 | 3, 5 | ax-bdim 14569 |
. . . 4
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7 | nfv 1528 |
. . . 4
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8 | nfv 1528 |
. . . 4
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9 | nfv 1528 |
. . . 4
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10 | nfv 1528 |
. . . 4
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11 | eleq1 2240 |
. . . . . 6
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12 | eleq1 2240 |
. . . . . 6
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13 | 11, 12 | imbi12d 234 |
. . . . 5
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14 | 13 | biimpd 144 |
. . . 4
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15 | eleq1 2240 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | eleq1 2240 |
. . . . . 6
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17 | 15, 16 | imbi12d 234 |
. . . . 5
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18 | 17 | biimprd 158 |
. . . 4
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19 | 6, 7, 8, 9, 10, 14, 18 | bdsetindis 14724 |
. . 3
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20 | 1, 19 | syl6 33 |
. 2
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21 | dfss2 3145 |
. 2
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22 | 20, 21 | imbitrrdi 162 |
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-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-ext 2159 ax-bdim 14569 ax-bdsetind 14723 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2740 df-un 3134 df-in 3136 df-ss 3143 df-sn 3599 df-suc 4372 df-bdc 14596 df-bj-ind 14682 |
This theorem is referenced by: bj-inf2vn 14729 |
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