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Mirrors > Home > ILE Home > Th. List > eleq1a | Unicode version |
Description: A transitive-type law relating membership and equality. (Contributed by NM, 9-Apr-1994.) |
Ref | Expression |
---|---|
eleq1a |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2240 |
. 2
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2 | 1 | biimprcd 160 |
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 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-17 1526 ax-ial 1534 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 df-clel 2173 |
This theorem is referenced by: elex22 2752 elex2 2753 reu6 2926 disjne 3476 ssimaex 5577 fnex 5738 f1ocnv2d 6074 mpoexw 6213 tfrlem8 6318 eroprf 6627 ac6sfi 6897 recclnq 7390 prnmaddl 7488 renegcl 8217 nn0ind-raph 9369 iccid 9924 4sqlem1 12385 4sqlem4 12389 opnneiid 13600 metrest 13942 coseq0negpitopi 14193 bj-nn0suc 14652 bj-inf2vnlem2 14659 bj-nn0sucALT 14666 |
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