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Mirrors > Home > NFE Home > Th. List > nfun | GIF version |
Description: Hypothesis builder for union. (Contributed by SF, 2-Jan-2018.) |
Ref | Expression |
---|---|
nfbool.1 | ⊢ ℲxA |
nfbool.2 | ⊢ ℲxB |
Ref | Expression |
---|---|
nfun | ⊢ Ⅎx(A ∪ B) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-un 3214 | . 2 ⊢ (A ∪ B) = ( ∼ A ⩃ ∼ B) | |
2 | nfbool.1 | . . . 4 ⊢ ℲxA | |
3 | 2 | nfcompl 3229 | . . 3 ⊢ Ⅎx ∼ A |
4 | nfbool.2 | . . . 4 ⊢ ℲxB | |
5 | 4 | nfcompl 3229 | . . 3 ⊢ Ⅎx ∼ B |
6 | 3, 5 | nfnin 3228 | . 2 ⊢ Ⅎx( ∼ A ⩃ ∼ B) |
7 | 1, 6 | nfcxfr 2486 | 1 ⊢ Ⅎx(A ∪ B) |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2476 ⩃ cnin 3204 ∼ ccompl 3205 ∪ cun 3207 |
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-nin 3211 df-compl 3212 df-un 3214 |
This theorem is referenced by: nfsymdif 3233 nfop 4604 |
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