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Mirrors > Home > MPE Home > Th. List > relwdom | Structured version Visualization version GIF version |
Description: Weak dominance is a relation. (Contributed by Stefan O'Rear, 11-Feb-2015.) |
Ref | Expression |
---|---|
relwdom | ⊢ Rel ≼* |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-wdom 8347 | . 2 ⊢ ≼* = {〈𝑥, 𝑦〉 ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)} | |
2 | 1 | relopabi 5167 | 1 ⊢ Rel ≼* |
Colors of variables: wff setvar class |
Syntax hints: ∨ wo 382 = wceq 1475 ∃wex 1695 ∅c0 3874 Rel wrel 5043 –onto→wfo 5802 ≼* cwdom 8345 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-opab 4644 df-xp 5044 df-rel 5045 df-wdom 8347 |
This theorem is referenced by: brwdom 8355 brwdomi 8356 brwdomn0 8357 wdomtr 8363 wdompwdom 8366 canthwdom 8367 brwdom3i 8371 unwdomg 8372 xpwdomg 8373 wdomfil 8767 isfin32i 9070 hsmexlem1 9131 hsmexlem3 9133 wdomac 9230 |
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