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Mirrors > Home > NFE Home > Th. List > elsncg | Unicode version |
Description: There is only one element in a singleton. Exercise 2 of [TakeutiZaring] p. 15 (generalized). (Contributed by NM, 13-Sep-1995.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
elsncg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2359 | . 2 | |
2 | df-sn 3741 | . 2 | |
3 | 1, 2 | elab2g 2987 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wceq 1642 wcel 1710 csn 3737 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-sn 3741 |
This theorem is referenced by: elsnc 3756 elsni 3757 snidg 3758 eltpg 3769 eldifsn 3839 opkth1g 4130 |
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