Theorem releqi 4721

Description: Equality inference for the relation predicate. (Contributed by NM, 8-Dec-2006.)

Hypothesis

Ref	Expression
releqi.1	|- A = B

Assertion

Ref	Expression
releqi	|- ( Rel A <-> Rel B )

Proof of Theorem releqi

Step	Hyp	Ref	Expression
1		releqi.1	. 2 |- A = B
2		releq 4720	. 2 |- ( A = B -> ( Rel A <-> Rel B ) )
3	1, 2	ax-mp 5	1 |- ( Rel A <-> Rel B )

Syntax hints:   <-> wb 105   = wceq 1363   Rel wrel 4643

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-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-11 1516  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-in 3147  df-ss 3154  df-rel 4645

This theorem is referenced by:  reliun  4759  reluni  4761  relint  4762  reldmmpo  6000  tfrlem6  6331  subrgdvds  13455  lssmex  13544  2idlmex  13691  psmetrel  14118  metrel  14138  xmetrel  14139  xmetf  14146  mopnrel  14237