Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ss0 | Unicode version |
Description: Any subset of the empty set is empty. Theorem 5 of [Suppes] p. 23. (Contributed by NM, 13-Aug-1994.) |
Ref | Expression |
---|---|
ss0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ss0b 3454 | . 2 | |
2 | 1 | biimpi 119 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wss 3121 c0 3414 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-dif 3123 df-in 3127 df-ss 3134 df-nul 3415 |
This theorem is referenced by: sseq0 3456 abf 3458 eq0rdv 3459 ssdisj 3471 0dif 3486 poirr2 5003 iotanul 5175 f00 5389 map0b 6665 phplem2 6831 php5dom 6841 sbthlem7 6940 fi0 6952 casefun 7062 caseinj 7066 djufun 7081 djuinj 7083 nnnninfeq 7104 exmidomni 7118 ixxdisj 9860 icodisj 9949 ioodisj 9950 uzdisj 10049 nn0disj 10094 fsum2dlemstep 11397 fprodssdc 11553 fprod2dlemstep 11585 ntrcls0 12925 |
Copyright terms: Public domain | W3C validator |