Theorem funeqi 4922

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 4921	. 2 |- ( A = B -> ( Fun A <-> Fun B ) )
3	1, 2	ax-mp 7	1 |- ( Fun A <-> Fun B )

Syntax hints:   <-> wb 98   = wceq 1243   Fun wfun 4896

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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-in 2924  df-ss 2931  df-br 3765  df-opab 3819  df-rel 4352  df-cnv 4353  df-co 4354  df-fun 4904

This theorem is referenced by:  funmpt  4938  funmpt2  4939  funprg  4949  funtpg  4950  funtp  4952  funcnvuni  4968  f1cnvcnv  5100  f1co  5101  fun11iun  5147  f10  5160  funoprabg  5600  mpt2fun  5603  ovidig  5618  tposfun  5875  rdgfun  5960  th3qcor  6210  ssdomg  6258