Theorem relopabv 4854

Description: A class of ordered pairs is a relation. For a version without a disjoint variable condition, see relopab 4856. (Contributed by SN, 8-Sep-2024.)

Assertion

Ref	Expression
relopabv	|- Rel { <. x , y >. | ph }

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem relopabv

Step	Hyp	Ref	Expression
1		eqid 2231	. 2 |- { <. x , y >. | ph } = { <. x , y >. | ph }
2	1	relopabiv 4853	1 |- Rel { <. x , y >. | ph }

Syntax hints:   {copab 4149   Rel wrel 4730

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-in 3206  df-ss 3213  df-opab 4151  df-xp 4731  df-rel 4732

This theorem is referenced by:  lgsquadlem3  15811