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Mirrors > Home > ILE Home > Th. List > csbeq2d | Unicode version |
Description: Formula-building deduction for class substitution. (Contributed by NM, 22-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.) |
Ref | Expression |
---|---|
csbeq2d.1 | |
csbeq2d.2 |
Ref | Expression |
---|---|
csbeq2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq2d.1 | . . . 4 | |
2 | csbeq2d.2 | . . . . 5 | |
3 | 2 | eleq2d 2209 | . . . 4 |
4 | 1, 3 | sbcbid 2966 | . . 3 |
5 | 4 | abbidv 2257 | . 2 |
6 | df-csb 3004 | . 2 | |
7 | df-csb 3004 | . 2 | |
8 | 5, 6, 7 | 3eqtr4g 2197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wnf 1436 wcel 1480 cab 2125 wsbc 2909 csb 3003 |
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-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 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-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-sbc 2910 df-csb 3004 |
This theorem is referenced by: csbeq2dv 3028 |
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