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Mirrors > Home > MPE Home > Th. List > mo2icl | Structured version Visualization version Unicode version |
Description: Theorem for inferring "at most one." (Contributed by NM, 17-Oct-1996.) |
Ref | Expression |
---|---|
mo2icl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq2 2472 |
. . . . . 6
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2 | 1 | imbi2d 322 |
. . . . 5
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3 | 2 | albidv 1777 |
. . . 4
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4 | 3 | imbi1d 323 |
. . 3
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5 | 19.8a 1945 |
. . . 4
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6 | mo2v 2316 |
. . . 4
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7 | 5, 6 | sylibr 217 |
. . 3
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8 | 4, 7 | vtoclg 3118 |
. 2
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9 | eqvisset 3064 |
. . . . . 6
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10 | 9 | imim2i 16 |
. . . . 5
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11 | 10 | con3rr3 143 |
. . . 4
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12 | 11 | alimdv 1773 |
. . 3
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13 | alnex 1675 |
. . . 4
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14 | exmo 2334 |
. . . . 5
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15 | 14 | ori 381 |
. . . 4
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16 | 13, 15 | sylbi 200 |
. . 3
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17 | 12, 16 | syl6 34 |
. 2
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18 | 8, 17 | pm2.61i 169 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-12 1943 ax-ext 2441 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-v 3058 |
This theorem is referenced by: invdisj 4404 opabiotafun 5948 fseqenlem2 8481 dfac2 8586 imasaddfnlem 15482 imasvscafn 15491 bnj149 29734 |
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