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Mirrors > Home > ILE Home > Th. List > eleq1i | Unicode version |
Description: Inference from equality to equivalence of membership. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eleq1i.1 |
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Ref | Expression |
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eleq1i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1i.1 |
. 2
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2 | eleq1 2177 |
. 2
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3 | 1, 2 | ax-mp 7 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1406 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-4 1470 ax-17 1489 ax-ial 1497 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-cleq 2108 df-clel 2111 |
This theorem is referenced by: eleq12i 2182 eqeltri 2187 intexrabim 4038 abssexg 4066 abnex 4328 snnex 4329 pwexb 4355 sucexb 4373 omex 4467 iprc 4765 dfse2 4870 fressnfv 5561 fnotovb 5768 f1stres 6011 f2ndres 6012 ottposg 6106 dftpos4 6114 frecabex 6249 oacl 6310 diffifi 6741 djuexb 6881 pitonn 7583 axicn 7598 pnfnre 7731 mnfnre 7732 0mnnnnn0 8913 nprmi 11651 txdis1cn 12289 xmeterval 12424 expcncf 12578 bj-sucexg 12812 |
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