Theorem funeqi 5293

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 5292	. 2 |- ( A = B -> ( Fun A <-> Fun B ) )
3	1, 2	ax-mp 5	1 |- ( Fun A <-> Fun B )

Syntax hints:   <-> wb 105   = wceq 1373   Fun wfun 5266

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-in 3172  df-ss 3179  df-br 4046  df-opab 4107  df-rel 4683  df-cnv 4684  df-co 4685  df-fun 5274

This theorem is referenced by:  funmpt  5310  funmpt2  5311  fununfun  5318  funprg  5325  funtpg  5326  funtp  5328  funcnvuni  5344  f1cnvcnv  5494  f1co  5495  fun11iun  5545  f10  5558  funopdmsn  5766  funoprabg  6046  mpofun  6049  ovidig  6065  tposfun  6348  tfri1dALT  6439  tfrcl  6452  rdgfun  6461  frecfun  6483  frecfcllem  6492  th3qcor  6728  ssdomg  6872  sbthlem7  7067  sbthlemi8  7068  casefun  7189  caseinj  7193  djufun  7208  djuinj  7210  ctssdccl  7215  axaddf  7983  axmulf  7984  fundm2domnop0  10992  strleund  12968  strleun  12969  1strbas  12982  2strbasg  12985  2stropg  12986  lidlmex  14270