![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > eqimss | Unicode version |
Description: Equality implies the subclass relation. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 21-Jun-2011.) |
Ref | Expression |
---|---|
eqimss |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqss 3172 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 1 | simplbi 274 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-in 3137 df-ss 3144 |
This theorem is referenced by: eqimss2 3212 uneqin 3388 sssnr 3755 sssnm 3756 ssprr 3758 sstpr 3759 snsspw 3766 pwpwssunieq 3977 elpwuni 3978 disjeq2 3986 disjeq1 3989 pwne 4162 pwssunim 4286 poeq2 4302 seeq1 4341 seeq2 4342 trsucss 4425 onsucelsucr 4509 xp11m 5069 funeq 5238 fnresdm 5327 fssxp 5385 ffdm 5388 fcoi1 5398 fof 5440 dff1o2 5468 fvmptss2 5593 fvmptssdm 5602 fprg 5701 dff1o6 5779 tposeq 6250 el2oss1o 6446 nntri1 6499 nntri2or2 6501 nnsseleq 6504 infnninf 7124 infnninfOLD 7125 nninfwlpoimlemg 7175 exmidontri2or 7244 frec2uzf1od 10408 hashinfuni 10759 setsresg 12502 setsslid 12515 strle1g 12567 cncnpi 13767 hmeores 13854 limcimolemlt 14172 recnprss 14195 0nninf 14792 nninfall 14797 |
Copyright terms: Public domain | W3C validator |