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Mirrors > Home > MPE Home > Th. List > sbcor | Structured version Visualization version Unicode version |
Description: Distribution of class substitution over disjunction. (Contributed by NM, 31-Dec-2016.) (Revised by NM, 17-Aug-2018.) |
Ref | Expression |
---|---|
sbcor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex 3445 | . 2 | |
2 | sbcex 3445 | . . 3 | |
3 | sbcex 3445 | . . 3 | |
4 | 2, 3 | jaoi 394 | . 2 |
5 | dfsbcq2 3438 | . . 3 | |
6 | dfsbcq2 3438 | . . . 4 | |
7 | dfsbcq2 3438 | . . . 4 | |
8 | 6, 7 | orbi12d 746 | . . 3 |
9 | sbor 2398 | . . 3 | |
10 | 5, 8, 9 | vtoclbg 3267 | . 2 |
11 | 1, 4, 10 | pm5.21nii 368 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wo 383 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-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: sbcori 33911 sbc3or 38738 |
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