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Mirrors > Home > MPE Home > Th. List > axc14 | Structured version Visualization version Unicode version |
Description: Axiom ax-c14 34176 is redundant if we assume ax-5 1839.
Remark 9.6 in
[Megill] p. 448 (p. 16 of the preprint),
regarding axiom scheme C14'.
Note that is a dummy variable introduced in the proof. Its purpose is to satisfy the distinct variable requirements of dveel2 2371 and ax-5 1839. By the end of the proof it has vanished, and the final theorem has no distinct variable requirements. (Contributed by NM, 29-Jun-1995.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
axc14 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbn1 2020 | . . . . 5 | |
2 | dveel2 2371 | . . . . 5 | |
3 | 1, 2 | hbim1 2125 | . . . 4 |
4 | elequ1 1997 | . . . . 5 | |
5 | 4 | imbi2d 330 | . . . 4 |
6 | 3, 5 | dvelim 2337 | . . 3 |
7 | nfa1 2028 | . . . . 5 | |
8 | 7 | nfn 1784 | . . . 4 |
9 | 8 | 19.21 2075 | . . 3 |
10 | 6, 9 | syl6ib 241 | . 2 |
11 | 10 | pm2.86d 107 | 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-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 |
This theorem is referenced by: (None) |
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