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Mirrors > Home > MPE Home > Th. List > ax12wdemo | Structured version Visualization version Unicode version |
Description: Example of an application
of ax12w 1918 that results in an instance of
ax-12 1944 for a contrived formula with mixed free and
bound variables,
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Ref | Expression |
---|---|
ax12wdemo |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elequ1 1905 |
. . 3
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2 | elequ2 1912 |
. . . . 5
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3 | 2 | cbvalvw 1889 |
. . . 4
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4 | 3 | a1i 11 |
. . 3
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5 | elequ1 1905 |
. . . . . 6
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6 | 5 | albidv 1778 |
. . . . 5
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7 | 6 | cbvalvw 1889 |
. . . 4
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8 | elequ2 1912 |
. . . . . 6
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9 | 8 | albidv 1778 |
. . . . 5
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10 | 9 | albidv 1778 |
. . . 4
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11 | 7, 10 | syl5bb 265 |
. . 3
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12 | 1, 4, 11 | 3anbi123d 1348 |
. 2
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13 | elequ2 1912 |
. . 3
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14 | 7 | a1i 11 |
. . 3
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15 | 13, 14 | 3anbi13d 1350 |
. 2
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16 | 12, 15 | ax12w 1918 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-8 1900 ax-9 1907 |
This theorem depends on definitions: df-bi 190 df-an 377 df-3an 993 df-ex 1675 |
This theorem is referenced by: (None) |
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