Theorem funeqi 5279

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 5278	. 2 |- ( A = B -> ( Fun A <-> Fun B ) )
3	1, 2	ax-mp 5	1 |- ( Fun A <-> Fun B )

Syntax hints:   <-> wb 105   = wceq 1364   Fun wfun 5252

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-in 3163  df-ss 3170  df-br 4034  df-opab 4095  df-rel 4670  df-cnv 4671  df-co 4672  df-fun 5260

This theorem is referenced by:  funmpt  5296  funmpt2  5297  funprg  5308  funtpg  5309  funtp  5311  funcnvuni  5327  f1cnvcnv  5474  f1co  5475  fun11iun  5525  f10  5538  funoprabg  6021  mpofun  6024  ovidig  6040  tposfun  6318  tfri1dALT  6409  tfrcl  6422  rdgfun  6431  frecfun  6453  frecfcllem  6462  th3qcor  6698  ssdomg  6837  sbthlem7  7029  sbthlemi8  7030  casefun  7151  caseinj  7155  djufun  7170  djuinj  7172  ctssdccl  7177  axaddf  7935  axmulf  7936  strleund  12781  strleun  12782  1strbas  12795  2strbasg  12797  2stropg  12798  lidlmex  14031