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Mirrors > Home > MPE Home > Th. List > csbeq2d | Structured version Visualization version 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 2687 | . . . 4 |
4 | 1, 3 | sbcbid 3489 | . . 3 |
5 | 4 | abbidv 2741 | . 2 |
6 | df-csb 3534 | . 2 | |
7 | df-csb 3534 | . 2 | |
8 | 5, 6, 7 | 3eqtr4g 2681 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wnf 1708 wcel 1990 cab 2608 wsbc 3435 csb 3533 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-sbc 3436 df-csb 3534 |
This theorem is referenced by: csbeq2dv 3992 poimirlem26 33435 |
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