Theorem relopabv 4823

Description: A class of ordered pairs is a relation. For a version without a disjoint variable condition, see relopab 4825. (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 2209	. 2 |- { <. x , y >. | ph } = { <. x , y >. | ph }
2	1	relopabiv 4822	1 |- Rel { <. x , y >. | ph }

Syntax hints:   {copab 4123   Rel wrel 4701

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 713  ax-5 1473  ax-7 1474  ax-gen 1475  ax-ie1 1519  ax-ie2 1520  ax-8 1530  ax-10 1531  ax-11 1532  ax-i12 1533  ax-bndl 1535  ax-4 1536  ax-17 1552  ax-i9 1556  ax-ial 1560  ax-i5r 1561  ax-ext 2191

This theorem depends on definitions:  df-bi 117  df-nf 1487  df-sb 1789  df-clab 2196  df-cleq 2202  df-clel 2205  df-nfc 2341  df-v 2781  df-in 3183  df-ss 3190  df-opab 4125  df-xp 4702  df-rel 4703

This theorem is referenced by:  lgsquadlem3  15723