Theorem releqi 4853

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 4852	. 2 |- ( A = B -> ( Rel A <-> Rel B ) )
3	1, 2	ax-mp 5	1 |- ( Rel A <-> Rel B )

Syntax hints:   <-> wb 105   = wceq 1402   Rel wrel 4774

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 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-in 3226  df-ss 3233  df-rel 4776

This theorem is referenced by:  reliun  4893  reluni  4895  relint  4896  reldmmpo  6190  tfrlem6  6577  opprringb  14359  reldvdsr  14371  subrgdvds  14516  rrgmex  14542  lssmex  14664  2idlmex  14810  psmetrel  15346  metrel  15366  xmetrel  15367  xmetf  15374  mopnrel  15465