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Mirrors > Home > MPE Home > Th. List > eupick | Structured version Visualization version Unicode version |
Description: Existential uniqueness "picks" a variable value for which another wff is true. If there is only one thing such that is true, and there is also an (actually the same one) such that and are both true, then implies regardless of . This theorem can be useful for eliminating existential quantifiers in a hypothesis. Compare Theorem *14.26 in [WhiteheadRussell] p. 192. (Contributed by NM, 10-Jul-1994.) |
Ref | Expression |
---|---|
eupick |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eumo 2499 | . 2 | |
2 | mopick 2535 | . 2 | |
3 | 1, 2 | sylan 488 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wex 1704 weu 2470 wmo 2471 |
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-10 2019 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ex 1705 df-nf 1710 df-eu 2474 df-mo 2475 |
This theorem is referenced by: eupicka 2537 eupickb 2538 reupick 3911 reupick3 3912 eusv2nf 4864 reusv2lem3 4871 copsexg 4956 funssres 5930 oprabid 6677 txcn 21429 isch3 28098 bnj849 30995 iotasbc 38620 |
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