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Mirrors > Home > ILE Home > Th. List > eleqtrri | Unicode version |
Description: Substitution of equal classes into membership relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eleqtrr.1 |
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eleqtrr.2 |
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Ref | Expression |
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eleqtrri |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleqtrr.1 |
. 2
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2 | eleqtrr.2 |
. . 3
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3 | 2 | eqcomi 2197 |
. 2
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4 | 1, 3 | eleqtri 2268 |
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 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-17 1537 ax-ial 1545 ax-ext 2175 |
This theorem depends on definitions: df-bi 117 df-cleq 2186 df-clel 2189 |
This theorem is referenced by: 3eltr4i 2275 undifexmid 4223 opi1 4262 opi2 4263 ordpwsucexmid 4603 peano1 4627 acexmidlemcase 5914 acexmidlem2 5916 0lt2o 6496 1lt2o 6497 0elixp 6785 ac6sfi 6956 ctssdccl 7172 exmidomni 7203 exmidonfinlem 7255 exmidfodomrlemr 7264 exmidfodomrlemrALT 7265 exmidaclem 7270 pw1ne3 7292 3nelsucpw1 7296 1lt2pi 7402 prarloclemarch2 7481 prarloclemlt 7555 prarloclemcalc 7564 suplocexprlemdisj 7782 suplocexprlemub 7785 pnfxr 8074 mnfxr 8078 fnpr2ob 12926 dveflem 14905 |
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