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Mirrors > Home > NFE Home > Th. List > rexsng | Unicode version |
Description: Restricted existential quantification over a singleton. (Contributed by NM, 29-Jan-2012.) |
Ref | Expression |
---|---|
ralsng.1 |
Ref | Expression |
---|---|
rexsng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexsns 3764 | . 2 | |
2 | ralsng.1 | . . 3 | |
3 | 2 | sbcieg 3078 | . 2 |
4 | 1, 3 | bitrd 244 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wceq 1642 wcel 1710 wrex 2615 wsbc 3046 csn 3737 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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-3an 936 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-rex 2620 df-v 2861 df-sbc 3047 df-sn 3741 |
This theorem is referenced by: rexsn 3768 rexprg 3776 rextpg 3778 iunxsng 4044 imasn 5018 |
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