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Mirrors > Home > MPE Home > Th. List > moabex | Structured version Visualization version Unicode version |
Description: "At most one" existence implies a class abstraction exists. (Contributed by NM, 30-Dec-1996.) |
Ref | Expression |
---|---|
moabex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mo2v 2307 |
. 2
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2 | abss 3466 |
. . . . 5
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3 | elsn 3950 |
. . . . . . 7
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4 | 3 | imbi2i 318 |
. . . . . 6
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5 | 4 | albii 1695 |
. . . . 5
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6 | 2, 5 | bitri 257 |
. . . 4
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7 | snex 4614 |
. . . . 5
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8 | 7 | ssex 4519 |
. . . 4
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9 | 6, 8 | sylbir 218 |
. . 3
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10 | 9 | exlimiv 1780 |
. 2
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11 | 1, 10 | sylbi 200 |
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 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-9 1900 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 ax-sep 4497 ax-nul 4506 ax-pr 4612 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-eu 2304 df-mo 2305 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-v 3015 df-dif 3375 df-un 3377 df-in 3379 df-ss 3386 df-nul 3700 df-sn 3937 df-pr 3939 |
This theorem is referenced by: rmorabex 4633 euabex 4634 |
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