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Mirrors > Home > MPE Home > Th. List > sbnfc2 | Unicode version |
Description: Two ways of expressing
"![]() ![]() |
Ref | Expression |
---|---|
sbnfc2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2927 |
. . . . 5
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2 | csbtt 3231 |
. . . . 5
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3 | 1, 2 | mpan 652 |
. . . 4
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4 | vex 2927 |
. . . . 5
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5 | csbtt 3231 |
. . . . 5
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6 | 4, 5 | mpan 652 |
. . . 4
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7 | 3, 6 | eqtr4d 2447 |
. . 3
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8 | 7 | alrimivv 1639 |
. 2
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9 | nfv 1626 |
. . 3
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10 | eleq2 2473 |
. . . . . 6
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11 | sbsbc 3133 |
. . . . . . 7
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12 | sbcel2g 3240 |
. . . . . . . 8
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13 | 1, 12 | ax-mp 8 |
. . . . . . 7
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14 | 11, 13 | bitri 241 |
. . . . . 6
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15 | sbsbc 3133 |
. . . . . . 7
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16 | sbcel2g 3240 |
. . . . . . . 8
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17 | 4, 16 | ax-mp 8 |
. . . . . . 7
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18 | 15, 17 | bitri 241 |
. . . . . 6
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19 | 10, 14, 18 | 3bitr4g 280 |
. . . . 5
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20 | 19 | 2alimi 1566 |
. . . 4
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21 | sbnf2 2165 |
. . . 4
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22 | 20, 21 | sylibr 204 |
. . 3
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23 | 9, 22 | nfcd 2543 |
. 2
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24 | 8, 23 | impbii 181 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: eusvnf 4685 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2393 |
This theorem depends on definitions: df-bi 178 df-an 361 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-clab 2399 df-cleq 2405 df-clel 2408 df-nfc 2537 df-v 2926 df-sbc 3130 df-csb 3220 |
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