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| Mirrors > Home > MPE Home > Th. List > Mathboxes > prtlem80 | Structured version Visualization version GIF version | ||
| Description: Lemma for prter2 38882. (Contributed by Rodolfo Medina, 17-Oct-2010.) |
| Ref | Expression |
|---|---|
| prtlem80 | ⊢ (𝐴 ∈ 𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴})) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | neldifsnd 4793 | 1 ⊢ (𝐴 ∈ 𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴})) |
| Colors of variables: wff setvar class |
| Syntax hints: ¬ wn 3 → wi 4 ∈ wcel 2108 ∖ cdif 3948 {csn 4626 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-ne 2941 df-v 3482 df-dif 3954 df-sn 4627 |
| This theorem is referenced by: (None) |
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