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Mirrors > Home > ILE Home > Th. List > csbco3g | Unicode version |
Description: Composition of two class substitutions. (Contributed by NM, 27-Nov-2005.) (Revised by Mario Carneiro, 11-Nov-2016.) |
Ref | Expression |
---|---|
sbcco3g.1 |
Ref | Expression |
---|---|
csbco3g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbnestg 3054 | . 2 | |
2 | elex 2697 | . . . 4 | |
3 | nfcvd 2282 | . . . . 5 | |
4 | sbcco3g.1 | . . . . 5 | |
5 | 3, 4 | csbiegf 3043 | . . . 4 |
6 | 2, 5 | syl 14 | . . 3 |
7 | 6 | csbeq1d 3010 | . 2 |
8 | 1, 7 | eqtrd 2172 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 cvv 2686 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-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-v 2688 df-sbc 2910 df-csb 3004 |
This theorem is referenced by: (None) |
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