Theorem mpteq2i 4105

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 4104	1 |- ( x e. A |-> B ) = ( x e. A |-> C )

Syntax hints:   = wceq 1364   e. wcel 2160   |-> cmpt 4079

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-ral 2473  df-opab 4080  df-mpt 4081

This theorem is referenced by:  frecsuc  6432  fodjuomni  7177  fodjumkv  7188  axcaucvg  7929  0tonninf  10470  1tonninf  10471  cbvsum  11400  cbvprod  11598  eirraplem  11816  cnmpt12f  14246  fsumcncntop  14516  dvef  14648  nninfsellemqall  15226  nninfomni  15230  exmidsbthr  15233