| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| 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 9605 | . 2 ⊢ ≼* = {〈𝑥, 𝑦〉 ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)} | |
| 2 | 1 | relopabiv 5830 | 1 ⊢ Rel ≼* |
| Colors of variables: wff setvar class |
| Syntax hints: ∨ wo 848 = wceq 1540 ∃wex 1779 ∅c0 4333 Rel wrel 5690 –onto→wfo 6559 ≼* cwdom 9604 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-ss 3968 df-opab 5206 df-xp 5691 df-rel 5692 df-wdom 9605 |
| This theorem is referenced by: brwdom 9607 brwdomi 9608 brwdomn0 9609 wdomtr 9615 wdompwdom 9618 canthwdom 9619 brwdom3i 9623 unwdomg 9624 xpwdomg 9625 wdomfil 10101 isfin32i 10405 hsmexlem1 10466 hsmexlem3 10468 wdomac 10567 |
| Copyright terms: Public domain | W3C validator |