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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 3952 | . . . . 5 | |
2 | csbconstg 2987 | . . . . . 6 | |
3 | csbconstg 2987 | . . . . . 6 | |
4 | 2, 3 | breq12d 3912 | . . . . 5 |
5 | 1, 4 | bitrd 187 | . . . 4 |
6 | 5 | opabbidv 3964 | . . 3 |
7 | csbopabg 3976 | . . 3 | |
8 | df-cnv 4517 | . . . 4 | |
9 | 8 | a1i 9 | . . 3 |
10 | 6, 7, 9 | 3eqtr4rd 2161 | . 2 |
11 | df-cnv 4517 | . . 3 | |
12 | 11 | csbeq2i 2999 | . 2 |
13 | 10, 12 | syl6eqr 2168 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wcel 1465 wsbc 2882 csb 2975 class class class wbr 3899 copab 3958 ccnv 4508 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-sbc 2883 df-csb 2976 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-cnv 4517 |
This theorem is referenced by: (None) |
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