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Mirrors > Home > MPE Home > Th. List > Mathboxes > prtlem80 | Structured version Visualization version GIF version |
Description: Lemma for prter2 36044. (Contributed by Rodolfo Medina, 17-Oct-2010.) |
Ref | Expression |
---|---|
prtlem80 | ⊢ (𝐴 ∈ 𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴})) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neldifsnd 4707 | 1 ⊢ (𝐴 ∈ 𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴})) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∈ wcel 2114 ∖ cdif 3916 {csn 4548 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2792 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2799 df-cleq 2813 df-clel 2891 df-nfc 2959 df-ne 3012 df-v 3483 df-dif 3922 df-sn 4549 |
This theorem is referenced by: (None) |
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