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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 2202 | . 2 | |
2 | 1 | biimprcd 159 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 |
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 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-17 1506 ax-ial 1514 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-cleq 2132 df-clel 2135 |
This theorem is referenced by: elex22 2701 elex2 2702 reu6 2873 disjne 3416 ssimaex 5482 fnex 5642 f1ocnv2d 5974 tfrlem8 6215 eroprf 6522 ac6sfi 6792 recclnq 7200 prnmaddl 7298 renegcl 8023 nn0ind-raph 9168 iccid 9708 opnneiid 12333 metrest 12675 coseq0negpitopi 12917 bj-nn0suc 13162 bj-inf2vnlem2 13169 bj-nn0sucALT 13176 |
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