Theorem cnveqi 4453

Description: Equality inference for converse. (Contributed by NM, 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 4452	. 2 ⊢ (A = B → ◡A = ◡B)
3	1, 2	ax-mp 7	1 ⊢ ◡A = ◡B

Syntax hints:   = wceq 1242  ^◡ccnv 4287

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-in 2918  df-ss 2925  df-br 3756  df-opab 3810  df-cnv 4296

This theorem is referenced by:  cnvxp  4685  xp0  4686  imainrect  4709  cnvcnv  4716  mptpreima  4757  co01  4778  coi2  4780  fcoi1  5013  fun11iun  5090  f1ocnvd  5644