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Mirrors > Home > ILE Home > Th. List > csbco | Unicode version |
Description: Composition law for
chained substitutions into a class.
Use the weaker csbcow 3051 when possible. (Contributed by NM, 10-Nov-2005.) (New usage is discouraged.) |
Ref | Expression |
---|---|
csbco |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-csb 3041 | . . . . . 6 | |
2 | 1 | abeq2i 2275 | . . . . 5 |
3 | 2 | sbcbii 3005 | . . . 4 |
4 | sbcco 2967 | . . . 4 | |
5 | 3, 4 | bitri 183 | . . 3 |
6 | 5 | abbii 2280 | . 2 |
7 | df-csb 3041 | . 2 | |
8 | df-csb 3041 | . 2 | |
9 | 6, 7, 8 | 3eqtr4i 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wcel 2135 cab 2150 wsbc 2946 csb 3040 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-sbc 2947 df-csb 3041 |
This theorem is referenced by: csbvarg 3068 csbnest1g 3095 zsumdc 11311 fsum3 11314 fsumsplitf 11335 |
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