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Mirrors > Home > MPE Home > Th. List > sbcal | Structured version Visualization version Unicode version |
Description: Move universal quantifier in and out of class substitution. (Contributed by NM, 31-Dec-2016.) (Revised by NM, 18-Aug-2018.) |
Ref | Expression |
---|---|
sbcal |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex 3445 | . 2 | |
2 | sbcex 3445 | . . 3 | |
3 | 2 | sps 2055 | . 2 |
4 | dfsbcq2 3438 | . . 3 | |
5 | dfsbcq2 3438 | . . . 4 | |
6 | 5 | albidv 1849 | . . 3 |
7 | sbal 2462 | . . 3 | |
8 | 4, 6, 7 | vtoclbg 3267 | . 2 |
9 | 1, 3, 8 | pm5.21nii 368 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wal 1481 wceq 1483 wsb 1880 wcel 1990 cvv 3200 wsbc 3435 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 df-sbc 3436 |
This theorem is referenced by: sbcabel 3517 sbcssg 4085 sbcfung 5912 bnj89 30787 bnj538OLD 30810 bnj110 30928 bnj611 30988 bnj1000 31011 bj-sbeq 32896 bj-sbceqgALT 32897 sbcalf 33917 frege70 38227 frege77 38234 frege116 38273 frege118 38275 trsbc 38750 |
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