Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > csbcnvg | Unicode version |
Description: Move class substitution in and out of the converse of a function. (Contributed by Thierry Arnoux, 8-Feb-2017.) |
Ref | Expression |
---|---|
csbcnvg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcbrg 3813 | . . . . 5 | |
2 | csbconstg 2864 | . . . . . 6 | |
3 | csbconstg 2864 | . . . . . 6 | |
4 | 2, 3 | breq12d 3777 | . . . . 5 |
5 | 1, 4 | bitrd 177 | . . . 4 |
6 | 5 | opabbidv 3823 | . . 3 |
7 | csbopabg 3835 | . . 3 | |
8 | df-cnv 4353 | . . . 4 | |
9 | 8 | a1i 9 | . . 3 |
10 | 6, 7, 9 | 3eqtr4rd 2083 | . 2 |
11 | df-cnv 4353 | . . 3 | |
12 | 11 | csbeq2i 2876 | . 2 |
13 | 10, 12 | syl6eqr 2090 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 wcel 1393 wsbc 2764 csb 2852 class class class wbr 3764 copab 3817 ccnv 4344 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-sbc 2765 df-csb 2853 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-cnv 4353 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |