![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > sseqtrd | Unicode version |
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004.) |
Ref | Expression |
---|---|
sseqtrd.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
sseqtrd.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
sseqtrd |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseqtrd.1 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | sseqtrd.2 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 2 | sseq2d 3057 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | 1, 3 | mpbid 146 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-11 1443 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-in 3008 df-ss 3015 |
This theorem is referenced by: sseqtr4d 3066 fssdmd 5189 resasplitss 5205 nnaword2 6289 erssxp 6331 phpm 6637 ioodisj 9473 tgcl 11827 basgen 11843 bastop1 11846 bastop2 11847 clsss2 11892 topssnei 11925 nninfalllemn 12201 |
Copyright terms: Public domain | W3C validator |