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Mirrors > Home > MPE Home > Th. List > nprrel | Structured version Visualization version GIF version |
Description: No proper class is related to anything via any relation. (Contributed by Roy F. Longton, 30-Jul-2005.) |
Ref | Expression |
---|---|
nprrel12.1 | ⊢ Rel 𝑅 |
nprrel.2 | ⊢ ¬ 𝐴 ∈ V |
Ref | Expression |
---|---|
nprrel | ⊢ ¬ 𝐴𝑅𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nprrel.2 | . 2 ⊢ ¬ 𝐴 ∈ V | |
2 | nprrel12.1 | . . 3 ⊢ Rel 𝑅 | |
3 | 2 | brrelex1i 5602 | . 2 ⊢ (𝐴𝑅𝐵 → 𝐴 ∈ V) |
4 | 1, 3 | mto 199 | 1 ⊢ ¬ 𝐴𝑅𝐵 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∈ wcel 2110 Vcvv 3494 class class class wbr 5058 Rel wrel 5554 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 ax-sep 5195 ax-nul 5202 ax-pr 5321 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rex 3144 df-rab 3147 df-v 3496 df-dif 3938 df-un 3940 df-in 3942 df-ss 3951 df-nul 4291 df-if 4467 df-sn 4561 df-pr 4563 df-op 4567 df-br 5059 df-opab 5121 df-xp 5555 df-rel 5556 |
This theorem is referenced by: (None) |
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