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Mirrors > Home > NFE Home > Th. List > ax467to6 | Unicode version |
Description: Re-derivation of ax-6o 2137 from ax467 2169. Note that ax-6o 2137 and ax-7 1734 are not used by the re-derivation. The use of alimi 1559 (which uses ax-4 2135) is allowed since we have already proved ax467to4 2170. (Contributed by NM, 19-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax467to6 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hba1-o 2149 |
. . . . . 6
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2 | 1 | con3i 127 |
. . . . 5
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3 | 2 | alimi 1559 |
. . . 4
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4 | 3 | sps-o 2159 |
. . 3
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5 | 4 | con3i 127 |
. 2
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6 | pm2.21 100 |
. 2
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7 | ax467 2169 |
. 2
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8 | 5, 6, 7 | 3syl 18 |
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 1546 ax-5 1557 ax-7 1734 ax-4 2135 ax-5o 2136 ax-6o 2137 |
This theorem is referenced by: ax467to7 2172 |
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