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Mirrors > Home > NFE Home > Th. List > dblcompl | Unicode version |
Description: Double complement law. (Contributed by SF, 10-Jan-2015.) |
Ref | Expression |
---|---|
dblcompl | ∼ ∼ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2862 | . . . 4 | |
2 | 1 | elcompl 3225 | . . 3 ∼ ∼ ∼ |
3 | 1 | elcompl 3225 | . . . 4 ∼ |
4 | 3 | con2bii 322 | . . 3 ∼ |
5 | 2, 4 | bitr4i 243 | . 2 ∼ ∼ |
6 | 5 | eqriv 2350 | 1 ∼ ∼ |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wceq 1642 wcel 1710 ∼ ccompl 3205 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 |
This theorem is referenced by: compleqb 3543 dfin5 3545 dfun4 3546 iunin 3547 iinun 3548 compl0 4071 sbthlem1 6203 |
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