Theorem funeqi 4972

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 4971	. 2 |- ( A = B -> ( Fun A <-> Fun B ) )
3	1, 2	ax-mp 7	1 |- ( Fun A <-> Fun B )

Syntax hints:   <-> wb 103   = wceq 1285   Fun wfun 4946

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-in 2988  df-ss 2995  df-br 3806  df-opab 3860  df-rel 4398  df-cnv 4399  df-co 4400  df-fun 4954

This theorem is referenced by:  funmpt  4988  funmpt2  4989  funprg  5000  funtpg  5001  funtp  5003  funcnvuni  5019  f1cnvcnv  5152  f1co  5153  fun11iun  5199  f10  5212  funoprabg  5652  mpt2fun  5655  ovidig  5670  tposfun  5930  tfri1dALT  6021  tfrcl  6034  rdgfun  6043  frecfun  6065  frecfcllem  6074  th3qcor  6298  ssdomg  6347