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Mirrors > Home > MPE Home > Th. List > relprcnfsupp | Structured version Visualization version GIF version |
Description: A proper class is never finitely supported. (Contributed by AV, 7-Jun-2019.) |
Ref | Expression |
---|---|
relprcnfsupp | ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 finSupp 𝑍) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relfsupp 9108 | . . 3 ⊢ Rel finSupp | |
2 | 1 | brrelex1i 5644 | . 2 ⊢ (𝐴 finSupp 𝑍 → 𝐴 ∈ V) |
3 | 2 | con3i 154 | 1 ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 finSupp 𝑍) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∈ wcel 2110 Vcvv 3431 class class class wbr 5079 finSupp cfsupp 9106 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2015 ax-8 2112 ax-9 2120 ax-ext 2711 ax-sep 5227 ax-nul 5234 ax-pr 5356 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-3an 1088 df-tru 1545 df-fal 1555 df-ex 1787 df-sb 2072 df-clab 2718 df-cleq 2732 df-clel 2818 df-ral 3071 df-rex 3072 df-rab 3075 df-v 3433 df-dif 3895 df-un 3897 df-in 3899 df-ss 3909 df-nul 4263 df-if 4466 df-sn 4568 df-pr 4570 df-op 4574 df-br 5080 df-opab 5142 df-xp 5596 df-rel 5597 df-fsupp 9107 |
This theorem is referenced by: fsuppres 9131 |
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