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Mirrors > Home > ILE Home > Th. List > rspc2gv | Unicode version |
Description: Restricted specialization with two quantifiers, using implicit substitution. (Contributed by BJ, 2-Dec-2021.) |
Ref | Expression |
---|---|
rspc2gv.1 |
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Ref | Expression |
---|---|
rspc2gv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2473 |
. 2
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2 | df-ral 2473 |
. . . . 5
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3 | 2 | imbi2i 226 |
. . . 4
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4 | 3 | albii 1481 |
. . 3
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5 | 19.21v 1884 |
. . . . . 6
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6 | 5 | bicomi 132 |
. . . . 5
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7 | 6 | albii 1481 |
. . . 4
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8 | impexp 263 |
. . . . . . 7
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9 | eleq1 2252 |
. . . . . . . . 9
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10 | eleq1 2252 |
. . . . . . . . 9
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11 | 9, 10 | bi2anan9 606 |
. . . . . . . 8
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12 | rspc2gv.1 |
. . . . . . . 8
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13 | 11, 12 | imbi12d 234 |
. . . . . . 7
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14 | 8, 13 | bitr3id 194 |
. . . . . 6
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15 | 14 | spc2gv 2843 |
. . . . 5
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16 | 15 | pm2.43a 51 |
. . . 4
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17 | 7, 16 | biimtrid 152 |
. . 3
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18 | 4, 17 | biimtrid 152 |
. 2
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19 | 1, 18 | biimtrid 152 |
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-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-ral 2473 df-v 2754 |
This theorem is referenced by: difinfsnlem 7129 difinfsn 7130 seqvalcd 10492 seqovcd 10496 qtopbasss 14498 apdiff 15275 |
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