Theorem reldmsets 13381

Description: The structure override operator is a proper operator. (Contributed by Stefan O'Rear, 29-Jan-2015.)

Assertion

Ref	Expression
reldmsets	⊢ Rel dom sSet

Proof of Theorem reldmsets

Dummy variables 𝑒 𝑠 are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-sets 13359	. 2 ⊢ sSet = (𝑠 ∈ V, 𝑒 ∈ V ↦ ((𝑠 ↾ (V ∖ dom {𝑒})) ∪ {𝑒}))
2	1	reldmmpo 6200	1 ⊢ Rel dom sSet

This proof depends on syntax axioms:  Vcvv 2821   ∖ cdif 3217   ∪ cun 3218  {csn 3709  dom cdm 4774   ↾ cres 4776  Rel wrel 4779   sSet csts 13350

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-14 2212  ax-ext 2220  ax-sep 4249  ax-pow 4311  ax-pr 4346

This proof depends on definitions:  df-bi 117  df-3an 1011  df-tru 1405  df-nf 1514  df-sb 1816  df-eu 2089  df-mo 2090  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-ral 2533  df-rex 2534  df-v 2823  df-un 3224  df-in 3226  df-ss 3233  df-pw 3690  df-sn 3715  df-pr 3716  df-op 3718  df-br 4131  df-opab 4193  df-xp 4780  df-rel 4781  df-dm 4784  df-oprab 6089  df-mpo 6090  df-sets 13359

This theorem is used by: (None)