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  6553  fodjuomni  7316  fodjumkv  7327  axcaucvg  8087  0tonninf  10662  1tonninf  10663  cbvsum  11871  cbvprod  12069  eirraplem  12288  znzrh2  14610  cnmpt12f  14960  fsumcncntop  15241  dvmptfsum  15399  dvef  15401  plyco  15433  plycj  15435  nninfsellemqall  16381  nninfomni  16385  nnnninfex  16388  exmidsbthr  16391