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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2233 | . 2 | |
2 | 1 | biimprcd 159 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 |
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 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-17 1519 ax-ial 1527 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-cleq 2163 df-clel 2166 |
This theorem is referenced by: elex22 2745 elex2 2746 reu6 2919 disjne 3468 ssimaex 5557 fnex 5718 f1ocnv2d 6053 mpoexw 6192 tfrlem8 6297 eroprf 6606 ac6sfi 6876 recclnq 7354 prnmaddl 7452 renegcl 8180 nn0ind-raph 9329 iccid 9882 4sqlem1 12340 4sqlem4 12344 opnneiid 12958 metrest 13300 coseq0negpitopi 13551 bj-nn0suc 13999 bj-inf2vnlem2 14006 bj-nn0sucALT 14013 |
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