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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-df-v | Structured version Visualization version Unicode version |
Description: Alternate definition of the universal class. Actually, the current definition df-v 3202 should be proved from this one, and vex 3203 should be proved from this proposed definition together with bj-vexwv 32857, which would remove from vex 3203 dependency on ax-13 2246 (see also comment of bj-vexw 32855). (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-df-v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfcleq 2616 | . 2 | |
2 | vex 3203 | . . 3 | |
3 | tru 1487 | . . . 4 | |
4 | 3 | bj-vexwv 32857 | . . 3 |
5 | 2, 4 | 2th 254 | . 2 |
6 | 1, 5 | mpgbir 1726 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wceq 1483 wtru 1484 wcel 1990 cab 2608 cvv 3200 |
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-12 2047 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-an 386 df-tru 1486 df-ex 1705 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 |
This theorem is referenced by: (None) |
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