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Mirrors > Home > ILE Home > Th. List > sbcco2 | Unicode version |
Description: A composition law for
class substitution. Importantly, ![]() ![]() |
Ref | Expression |
---|---|
sbcco2.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
sbcco2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbsbc 2762 |
. 2
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2 | nfv 1418 |
. . 3
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3 | sbcco2.1 |
. . . . 5
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4 | 3 | equcoms 1591 |
. . . 4
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5 | dfsbcq 2760 |
. . . . 5
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6 | 5 | bicomd 129 |
. . . 4
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7 | 4, 6 | syl 14 |
. . 3
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8 | 2, 7 | sbie 1671 |
. 2
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9 | 1, 8 | bitr3i 175 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-sbc 2759 |
This theorem is referenced by: (None) |
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