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Mirrors > Home > ILE Home > Th. List > sbceq1d | 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 |
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Ref | Expression |
---|---|
sbceq1d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbceq1d.1 |
. 2
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2 | dfsbcq 2915 |
. 2
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3 | 1, 2 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
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 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-17 1507 ax-ial 1515 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-cleq 2133 df-clel 2136 df-sbc 2914 |
This theorem is referenced by: sbceq1dd 2919 rexrnmpt 5571 findcard2 6791 findcard2s 6792 ac6sfi 6800 nn1suc 8763 uzind4s 9412 uzind4s2 9413 fzrevral 9916 fzshftral 9919 cjth 10650 prmind2 11837 bj-bdfindes 13318 bj-findes 13350 |
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