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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 2227 | . 2 | |
2 | 1 | biimprcd 159 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 wcel 2135 |
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 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-17 1513 ax-ial 1521 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-cleq 2157 df-clel 2160 |
This theorem is referenced by: elex22 2736 elex2 2737 reu6 2910 disjne 3457 ssimaex 5541 fnex 5701 f1ocnv2d 6036 tfrlem8 6277 eroprf 6585 ac6sfi 6855 recclnq 7324 prnmaddl 7422 renegcl 8150 nn0ind-raph 9299 iccid 9852 opnneiid 12711 metrest 13053 coseq0negpitopi 13304 bj-nn0suc 13687 bj-inf2vnlem2 13694 bj-nn0sucALT 13701 |
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