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Mirrors > Home > ILE Home > Th. List > ax9vsep | Unicode version |
Description: Derive a weakened version of ax-9 1464, where and must be distinct, from Separation ax-sep 3896 and Extensionality ax-ext 2063. In intuitionistic logic a9evsep 3900 is stronger and also holds. (Contributed by NM, 12-Nov-2013.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax9vsep |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9evsep 3900 | . 2 | |
2 | exalim 1431 | . 2 | |
3 | 1, 2 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wal 1282 wceq 1284 wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-ial 1467 ax-ext 2063 ax-sep 3896 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-fal 1290 |
This theorem is referenced by: (None) |
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