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Mirrors > Home > MPE Home > Th. List > neldifsnd | Structured version Visualization version GIF version |
Description: The class 𝐴 is not in (𝐵 ∖ {𝐴}). Deduction form. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
neldifsnd | ⊢ (𝜑 → ¬ 𝐴 ∈ (𝐵 ∖ {𝐴})) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neldifsn 4262 | . 2 ⊢ ¬ 𝐴 ∈ (𝐵 ∖ {𝐴}) | |
2 | 1 | a1i 11 | 1 ⊢ (𝜑 → ¬ 𝐴 ∈ (𝐵 ∖ {𝐴})) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∈ wcel 1977 ∖ cdif 3537 {csn 4125 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ne 2782 df-v 3175 df-dif 3543 df-sn 4126 |
This theorem is referenced by: difsnb 4278 fsnunf2 6357 rpnnen2lem9 14790 fprodfvdvdsd 14896 ramub1lem1 15568 ramub1lem2 15569 prmdvdsprmo 15584 acsfiindd 17000 gsummgp0 18431 islindf4 19996 gsummatr01lem3 20282 omsmeas 29712 onint1 31618 poimirlem30 32609 prtlem80 33163 gneispace0nelrn3 37460 fsumnncl 38638 fsumsplit1 38639 hoidmv1lelem2 39482 hspmbllem1 39516 hspmbllem2 39517 fsumsplitsndif 40372 nbgrnself 40583 mgpsumunsn 41933 |
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