Theorem cnveqi 4888

Description: Equality inference for converse. (Contributed by set.mm contributors, 23-Dec-2008.)

Hypothesis

Ref	Expression
cnveqi.1	⊢ A = B

Assertion

Ref	Expression
cnveqi	⊢ ◡A = ◡B

Proof of Theorem cnveqi

Step	Hyp	Ref	Expression
1		cnveqi.1	. 2 ⊢ A = B
2		cnveq 4887	. 2 ⊢ (A = B → ◡A = ◡B)
3	1, 2	ax-mp 5	1 ⊢ ◡A = ◡B

Syntax hints:   = wceq 1642  ^◡ccnv 4772

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-ss 3260  df-opab 4624  df-br 4641  df-cnv 4786

This theorem is referenced by:  cnvin  5036  cnvxp  5044  xp0  5045  cnvtr  5099  fun11iun  5306  mptpreima  5683  f1od  5727  cnvpprod  5842  scancan  6332