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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 4041 | . . . . 5 | |
2 | csbconstg 3063 | . . . . . 6 | |
3 | csbconstg 3063 | . . . . . 6 | |
4 | 2, 3 | breq12d 4000 | . . . . 5 |
5 | 1, 4 | bitrd 187 | . . . 4 |
6 | 5 | opabbidv 4053 | . . 3 |
7 | csbopabg 4065 | . . 3 | |
8 | df-cnv 4617 | . . . 4 | |
9 | 8 | a1i 9 | . . 3 |
10 | 6, 7, 9 | 3eqtr4rd 2214 | . 2 |
11 | df-cnv 4617 | . . 3 | |
12 | 11 | csbeq2i 3076 | . 2 |
13 | 10, 12 | eqtr4di 2221 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 wsbc 2955 csb 3049 class class class wbr 3987 copab 4047 ccnv 4608 |
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 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-3an 975 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-sbc 2956 df-csb 3050 df-un 3125 df-sn 3587 df-pr 3588 df-op 3590 df-br 3988 df-opab 4049 df-cnv 4617 |
This theorem is referenced by: (None) |
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