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Mathbox for Andrew Salmon |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > axc5c4c711 | Structured version Visualization version Unicode version |
Description: Proof of a theorem that can act as a sole axiom for pure predicate calculus with ax-gen 1680 as the inference rule. This proof extends the idea of axc5c711 32535 and related theorems. (Contributed by Andrew Salmon, 14-Jul-2011.) |
Ref | Expression |
---|---|
axc5c4c711 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axc4 1949 |
. . 3
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2 | hbn1 1927 |
. . . . 5
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3 | axc7 1950 |
. . . . . 6
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4 | 3 | con1i 134 |
. . . . 5
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5 | 2, 4 | alrimih 1704 |
. . . 4
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6 | ax-11 1931 |
. . . 4
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7 | 5, 6 | syl 17 |
. . 3
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8 | 1, 7 | nsyl4 149 |
. 2
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9 | pm2.21 112 |
. . . 4
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10 | 9 | spsd 1956 |
. . 3
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11 | 10, 1 | ja 166 |
. 2
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12 | 8, 11 | ja 166 |
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-10 1926 ax-11 1931 ax-12 1944 |
This theorem depends on definitions: df-bi 190 df-an 377 df-ex 1675 |
This theorem is referenced by: axc5c4c711toc5 36798 axc5c4c711toc4 36799 axc5c4c711toc7 36800 axc5c4c711to11 36801 |
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