Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > csbima12g | Unicode version |
Description: Move class substitution in and out of the image of a function. (Contributed by FL, 15-Dec-2006.) (Proof shortened by Mario Carneiro, 4-Dec-2016.) |
Ref | Expression |
---|---|
csbima12g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq1 3006 | . . 3 | |
2 | csbeq1 3006 | . . . 4 | |
3 | csbeq1 3006 | . . . 4 | |
4 | 2, 3 | imaeq12d 4882 | . . 3 |
5 | 1, 4 | eqeq12d 2154 | . 2 |
6 | vex 2689 | . . 3 | |
7 | nfcsb1v 3035 | . . . 4 | |
8 | nfcsb1v 3035 | . . . 4 | |
9 | 7, 8 | nfima 4889 | . . 3 |
10 | csbeq1a 3012 | . . . 4 | |
11 | csbeq1a 3012 | . . . 4 | |
12 | 10, 11 | imaeq12d 4882 | . . 3 |
13 | 6, 9, 12 | csbief 3044 | . 2 |
14 | 5, 13 | vtoclg 2746 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 csb 3003 cima 4542 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rab 2425 df-v 2688 df-sbc 2910 df-csb 3004 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-xp 4545 df-cnv 4547 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |