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| Mirrors > Home > MPE Home > Th. List > ax10 | Structured version Unicode version | |
| Description: Rederivation of axiom ax-10 1781 from ax-c7 2204 and other older axioms. See axc7 1805 for the derivation of ax-c7 2204 from ax-10 1781. (Contributed by NM, 23-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| ax10 |
        |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-c4 2203 |
. . 3
| |
| 2 | ax-c5 2202 |
. . . 4
| |
| 3 | ax-c4 2203 |
. . . . 5
| |
| 4 | id 22 |
. . . . 5
| |
| 5 | 3, 4 | mpg 1598 |
. . . 4
|
| 6 | 2, 5 | nsyl 121 |
. . 3
|
| 7 | 1, 6 | mpg 1598 |
. 2
|
| 8 | ax-c7 2204 |
. 2
| |
| 9 | 7, 8 | nsyl4 142 |
1
|
| Colors of variables: wff setvar class |
| Syntax hints: wn 3
wi 4
wal 1372 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1596 ax-c5 2202 ax-c4 2203 ax-c7 2204 |
| This theorem is referenced by: hba1-o 2216 axc5c711 2236 equidq 2242 |
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