Theorem funeqi 4865

Description: Equality inference for the function predicate. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypothesis

Ref	Expression
funeqi.1	|- A = B

Assertion

Ref	Expression
funeqi	|- ( Fun A <-> Fun B)

Proof of Theorem funeqi

Step	Hyp	Ref	Expression
1		funeqi.1	. 2 |- A = B
2		funeq 4864	. 2 |- (A = B -> ( Fun A <-> Fun B))
3	1, 2	ax-mp 7	1 |- ( Fun A <-> Fun B)

Syntax hints:   <-> wb 98   = wceq 1242   Fun wfun 4839

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-bndl 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-rel 4295  df-cnv 4296  df-co 4297  df-fun 4847

This theorem is referenced by:  funmpt  4881  funmpt2  4882  funprg  4892  funtpg  4893  funtp  4895  funcnvuni  4911  f1cnvcnv  5043  f1co  5044  fun11iun  5090  f10  5103  funoprabg  5542  mpt2fun  5545  ovidig  5560  tposfun  5816  rdgfun  5900  th3qcor  6146  ssdomg  6194