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Mirrors > Home > NFE Home > Th. List > csbco | Unicode version |
Description: Composition law for chained substitutions into a class. (Contributed by NM, 10-Nov-2005.) |
Ref | Expression |
---|---|
csbco |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-csb 3137 | . . . . . 6 | |
2 | 1 | abeq2i 2460 | . . . . 5 |
3 | 2 | sbcbii 3101 | . . . 4 |
4 | sbcco 3068 | . . . 4 | |
5 | 3, 4 | bitri 240 | . . 3 |
6 | 5 | abbii 2465 | . 2 |
7 | df-csb 3137 | . 2 | |
8 | df-csb 3137 | . 2 | |
9 | 6, 7, 8 | 3eqtr4i 2383 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1642 wcel 1710 cab 2339 wsbc 3046 csb 3136 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-sbc 3047 df-csb 3137 |
This theorem is referenced by: csbvarg 3163 csbnest1g 3188 eqerlem 5960 |
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