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Mirrors > Home > ILE Home > Th. List > sbceq1dd | 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 2960 | . 2 |
4 | 1, 3 | mpbid 146 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wsbc 2955 |
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-5 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-17 1519 ax-ial 1527 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-cleq 2163 df-clel 2166 df-sbc 2956 |
This theorem is referenced by: prmind2 12074 |
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