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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 1646 and substitution for class variables df-sbc 2765. Unlike Quine, we use a different syntax for each in order to avoid overloading it. See remarks in dfsbcq 2766. (Contributed by NM, 31-Dec-2016.) |
Ref | Expression |
---|---|
dfsbcq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2100 | . 2 | |
2 | df-clab 2027 | . 2 | |
3 | df-sbc 2765 | . . 3 | |
4 | 3 | bicomi 123 | . 2 |
5 | 1, 2, 4 | 3bitr3g 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wcel 1393 wsb 1645 cab 2026 wsbc 2764 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-clab 2027 df-cleq 2033 df-clel 2036 df-sbc 2765 |
This theorem is referenced by: sbsbc 2768 sbc8g 2771 sbceq1a 2773 sbc5 2787 sbcng 2803 sbcimg 2804 sbcan 2805 sbcang 2806 sbcor 2807 sbcorg 2808 sbcbig 2809 sbcal 2810 sbcalg 2811 sbcex2 2812 sbcexg 2813 sbc3ang 2820 sbcel1gv 2821 sbctt 2824 sbcralt 2834 sbcrext 2835 sbcralg 2836 sbcreug 2838 rspsbc 2840 rspesbca 2842 sbcel12g 2865 sbceqg 2866 sbcbrg 3813 csbopabg 3835 opelopabsb 3997 findes 4326 iota4 4885 csbiotag 4895 csbriotag 5480 nn0ind-raph 8355 uzind4s 8533 |
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