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Mirrors > Home > MPE Home > Th. List > sbceq1dd | Structured version Visualization version Unicode version |
Description: Equality theorem for class substitution. (Contributed by Mario Carneiro, 9-Feb-2017.) (Revised by NM, 30-Jun-2018.) |
Ref | Expression |
---|---|
sbceq1d.1 | |
sbceq1dd.2 |
Ref | Expression |
---|---|
sbceq1dd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbceq1dd.2 | . 2 | |
2 | sbceq1d.1 | . . 3 | |
3 | 2 | sbceq1d 3440 | . 2 |
4 | 1, 3 | mpbid 222 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wsbc 3435 |
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-ext 2602 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-cleq 2615 df-clel 2618 df-sbc 3436 |
This theorem is referenced by: prmind2 15398 sdclem2 33538 sbceq1ddi 33928 |
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