Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 1721 and substitution for class variables df-sbc 2883. Unlike Quine, we use a different syntax for each in order to avoid overloading it. See remarks in dfsbcq 2884. (Contributed by NM, 31-Dec-2016.) |
Ref | Expression |
---|---|
dfsbcq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2180 | . 2 | |
2 | df-clab 2104 | . 2 | |
3 | df-sbc 2883 | . . 3 | |
4 | 3 | bicomi 131 | . 2 |
5 | 1, 2, 4 | 3bitr3g 221 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1316 wcel 1465 wsb 1720 cab 2103 wsbc 2882 |
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 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-clab 2104 df-cleq 2110 df-clel 2113 df-sbc 2883 |
This theorem is referenced by: sbsbc 2886 sbc8g 2889 sbceq1a 2891 sbc5 2905 sbcng 2921 sbcimg 2922 sbcan 2923 sbcang 2924 sbcor 2925 sbcorg 2926 sbcbig 2927 sbcal 2932 sbcalg 2933 sbcex2 2934 sbcexg 2935 sbcel1v 2943 sbctt 2947 sbcralt 2957 sbcrext 2958 sbcralg 2959 sbcreug 2961 rspsbc 2963 rspesbca 2965 sbcel12g 2988 sbceqg 2989 sbcbrg 3952 csbopabg 3976 opelopabsb 4152 findes 4487 iota4 5076 csbiotag 5086 csbriotag 5710 nn0ind-raph 9136 uzind4s 9353 bezoutlemmain 11613 bezoutlemex 11616 |
Copyright terms: Public domain | W3C validator |