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Mirrors > Home > ILE Home > Th. List > eqeq12i | Unicode version |
Description: A useful inference for substituting definitions into an equality. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
eqeq12i.1 | |
eqeq12i.2 |
Ref | Expression |
---|---|
eqeq12i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq12i.1 | . 2 | |
2 | eqeq12i.2 | . 2 | |
3 | eqeq12 2183 | . 2 | |
4 | 1, 2, 3 | mp2an 424 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1348 |
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-4 1503 ax-17 1519 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-cleq 2163 |
This theorem is referenced by: rabbi 2647 sbceqg 3065 preqr2g 3754 preqr2 3756 otth 4227 rncoeq 4884 eqfnov 5959 mpo2eqb 5962 f1o2ndf1 6207 ecopovsym 6609 sq11i 10565 pwle2 14031 |
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