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Mirrors > Home > MPE Home > Th. List > Mathboxes > prtlem80 | Structured version Visualization version GIF version |
Description: Lemma for prter2 37393. (Contributed by Rodolfo Medina, 17-Oct-2010.) |
Ref | Expression |
---|---|
prtlem80 | ⊢ (𝐴 ∈ 𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴})) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neldifsnd 4757 | 1 ⊢ (𝐴 ∈ 𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴})) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∈ wcel 2107 ∖ cdif 3911 {csn 4590 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-ne 2941 df-v 3449 df-dif 3917 df-sn 4591 |
This theorem is referenced by: (None) |
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