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Mirrors > Home > MPE Home > Th. List > 3brtr3i | Structured version Visualization version Unicode version |
Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999.) |
Ref | Expression |
---|---|
3brtr3.1 |
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3brtr3.2 |
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3brtr3.3 |
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Ref | Expression |
---|---|
3brtr3i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3brtr3.2 |
. . 3
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2 | 3brtr3.1 |
. . 3
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3 | 1, 2 | eqbrtrri 4424 |
. 2
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4 | 3brtr3.3 |
. 2
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5 | 3, 4 | breqtri 4426 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-rab 2746 df-v 3047 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-br 4403 |
This theorem is referenced by: supsrlem 9535 ef01bndlem 14238 pige3 23472 log2ublem1 23872 log2ub 23875 ppiublem1 24130 logfacrlim2 24154 chebbnd1 24310 nmoptri2i 27752 problem5 30301 fouriersw 38095 |
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