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Mirrors > Home > NFE Home > Th. List > csbeq2d | Unicode version |
Description: Formula-building deduction rule 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 2420 | . . . 4 |
4 | 1, 3 | sbcbid 3099 | . . 3 |
5 | 4 | abbidv 2467 | . 2 |
6 | df-csb 3137 | . 2 | |
7 | df-csb 3137 | . 2 | |
8 | 5, 6, 7 | 3eqtr4g 2410 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wnf 1544 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-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-sbc 3047 df-csb 3137 |
This theorem is referenced by: csbeq2dv 3161 |
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