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| Mirrors > Home > MPE Home > Th. List > Mathboxes > ax10fromc7 | Structured version Visualization version Unicode version | ||
| Description: Rederivation of axiom ax-10 2019 from ax-c7 34170, ax-c4 34169, ax-c5 34168, ax-gen 1722 and propositional calculus. See axc7 2132 for the derivation of ax-c7 34170 from ax-10 2019. (Contributed by NM, 23-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| ax10fromc7 |
        |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-c4 34169 |
. . 3
| |
| 2 | ax-c5 34168 |
. . . 4
| |
| 3 | ax-c4 34169 |
. . . . 5
| |
| 4 | id 22 |
. . . . 5
| |
| 5 | 3, 4 | mpg 1724 |
. . . 4
|
| 6 | 2, 5 | nsyl 135 |
. . 3
|
| 7 | 1, 6 | mpg 1724 |
. 2
|
| 8 | ax-c7 34170 |
. 2
| |
| 9 | 7, 8 | nsyl4 156 |
1
|
| Colors of variables: wff setvar class |
| Syntax hints: wn 3
wi 4
wal 1481 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-c5 34168 ax-c4 34169 ax-c7 34170 |
| This theorem is referenced by: hba1-o 34182 axc5c711 34203 equidq 34209 |
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