Theorem mpteq2i 4069

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 4068	1 |- ( x e. A |-> B ) = ( x e. A |-> C )

Syntax hints:   = wceq 1343   e. wcel 2136   |-> cmpt 4043

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-11 1494  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-ral 2449  df-opab 4044  df-mpt 4045

This theorem is referenced by:  frecsuc  6375  fodjuomni  7113  fodjumkv  7124  axcaucvg  7841  0tonninf  10374  1tonninf  10375  cbvsum  11301  cbvprod  11499  eirraplem  11717  cnmpt12f  12926  fsumcncntop  13196  dvef  13328  nninfsellemqall  13895  nninfomni  13899  exmidsbthr  13902