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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 |
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eqeq12i.2 |
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Ref | Expression |
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eqeq12i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq12i.1 |
. 2
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2 | eqeq12i.2 |
. 2
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3 | eqeq12 2190 |
. 2
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4 | 1, 2, 3 | mp2an 426 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 ax-4 1510 ax-17 1526 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 |
This theorem is referenced by: rabbi 2655 sbceqg 3075 preqr2g 3769 preqr2 3771 otth 4244 rncoeq 4902 eqfnov 5983 mpo2eqb 5986 f1o2ndf1 6231 ecopovsym 6633 sq11i 10612 pwle2 14787 |
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