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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ax10 | Structured version Visualization version Unicode version |
Description: Rederivation of axiom ax-10 1925 from ax-c7 32501 and other older axioms. See axc7 1949 for the derivation of ax-c7 32501 from ax-10 1925. (Contributed by NM, 23-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax10 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-c4 32500 |
. . 3
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2 | ax-c5 32499 |
. . . 4
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3 | ax-c4 32500 |
. . . . 5
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4 | id 22 |
. . . . 5
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5 | 3, 4 | mpg 1681 |
. . . 4
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6 | 2, 5 | nsyl 126 |
. . 3
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7 | 1, 6 | mpg 1681 |
. 2
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8 | ax-c7 32501 |
. 2
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9 | 7, 8 | nsyl4 149 |
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-c5 32499 ax-c4 32500 ax-c7 32501 |
This theorem is referenced by: hba1-o 32513 axc5c711 32533 equidq 32539 |
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