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Mirrors > Home > ILE Home > Th. List > ax9vsep | Unicode version |
Description: Derive a weakened version of ax-9 1496, where and must be distinct, from Separation ax-sep 4016 and Extensionality ax-ext 2099. In intuitionistic logic a9evsep 4020 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 4020 | . 2 | |
2 | exalim 1463 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wal 1314 wceq 1316 wex 1453 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 588 ax-in2 589 ax-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-ial 1499 ax-ext 2099 ax-sep 4016 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-fal 1322 |
This theorem is referenced by: (None) |
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