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Mirrors > Home > MPE Home > Th. List > Mathboxes > prtlem80 | Structured version Visualization version GIF version |
Description: Lemma for prter2 36177. (Contributed by Rodolfo Medina, 17-Oct-2010.) |
Ref | Expression |
---|---|
prtlem80 | ⊢ (𝐴 ∈ 𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴})) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neldifsnd 4686 | 1 ⊢ (𝐴 ∈ 𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴})) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∈ wcel 2111 ∖ cdif 3878 {csn 4525 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1782 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-ne 2988 df-v 3443 df-dif 3884 df-sn 4526 |
This theorem is referenced by: (None) |
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