Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sbcsng | Unicode version |
Description: Substitution expressed in terms of quantification over a singleton. (Contributed by NM, 14-Dec-2005.) (Revised by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
sbcsng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralsns 3557 | . 2 | |
2 | 1 | bicomd 140 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wcel 1480 wral 2414 wsbc 2904 csn 3522 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-v 2683 df-sbc 2905 df-sn 3528 |
This theorem is referenced by: zsupcllemstep 11627 |
Copyright terms: Public domain | W3C validator |