Theorem mpteq2i 4171

Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013.)

Hypothesis

Ref	Expression
mpteq2i.1	|- B = C

Assertion

Ref	Expression
mpteq2i	|- ( x e. A |-> B ) = ( x e. A |-> C )

Proof of Theorem mpteq2i

Step	Hyp	Ref	Expression
1		mpteq2i.1	. . 3 |- B = C
2	1	a1i 9	. 2 |- ( x e. A -> B = C )
3	2	mpteq2ia 4170	1 |- ( x e. A |-> B ) = ( x e. A |-> C )

Syntax hints:   = wceq 1395   e. wcel 2200   |-> cmpt 4145

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-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-ral 2513  df-opab 4146  df-mpt 4147

This theorem is referenced by:  frecsuc  6559  fodjuomni  7327  fodjumkv  7338  axcaucvg  8098  0tonninf  10674  1tonninf  10675  cbvsum  11887  cbvprod  12085  eirraplem  12304  znzrh2  14626  cnmpt12f  14976  fsumcncntop  15257  dvmptfsum  15415  dvef  15417  plyco  15449  plycj  15451  nninfsellemqall  16469  nninfomni  16473  nnnninfex  16476  exmidsbthr  16479