Theorem relopabv 4846

Description: A class of ordered pairs is a relation. For a version without a disjoint variable condition, see relopab 4848. (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 2229	. 2 |- { <. x , y >. | ph } = { <. x , y >. | ph }
2	1	relopabiv 4845	1 |- Rel { <. x , y >. | ph }

Syntax hints:   {copab 4144   Rel wrel 4724

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-in 3203  df-ss 3210  df-opab 4146  df-xp 4725  df-rel 4726

This theorem is referenced by:  lgsquadlem3  15766