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Mirrors > Home > ILE Home > Th. List > dfsbcq2 | Unicode version |
Description: This theorem, which is similar to Theorem 6.7 of [Quine] p. 42 and holds under both our definition and Quine's, relates logic substitution df-sb 1704 and substitution for class variables df-sbc 2863. Unlike Quine, we use a different syntax for each in order to avoid overloading it. See remarks in dfsbcq 2864. (Contributed by NM, 31-Dec-2016.) |
Ref | Expression |
---|---|
dfsbcq2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2162 |
. 2
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2 | df-clab 2087 |
. 2
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3 | df-sbc 2863 |
. . 3
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4 | 3 | bicomi 131 |
. 2
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5 | 1, 2, 4 | 3bitr3g 221 |
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 1391 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-4 1455 ax-17 1474 ax-ial 1482 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-clab 2087 df-cleq 2093 df-clel 2096 df-sbc 2863 |
This theorem is referenced by: sbsbc 2866 sbc8g 2869 sbceq1a 2871 sbc5 2885 sbcng 2901 sbcimg 2902 sbcan 2903 sbcang 2904 sbcor 2905 sbcorg 2906 sbcbig 2907 sbcal 2912 sbcalg 2913 sbcex2 2914 sbcexg 2915 sbcel1v 2923 sbctt 2927 sbcralt 2937 sbcrext 2938 sbcralg 2939 sbcreug 2941 rspsbc 2943 rspesbca 2945 sbcel12g 2968 sbceqg 2969 sbcbrg 3924 csbopabg 3946 opelopabsb 4120 findes 4455 iota4 5042 csbiotag 5052 csbriotag 5674 nn0ind-raph 9020 uzind4s 9235 bezoutlemmain 11479 bezoutlemex 11482 |
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