Theorem mpteq2i 4074

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 4073	1 |- ( x e. A |-> B ) = ( x e. A |-> C )

Syntax hints:   = wceq 1348   e. wcel 2141   |-> cmpt 4048

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 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-ral 2453  df-opab 4049  df-mpt 4050

This theorem is referenced by:  frecsuc  6383  fodjuomni  7121  fodjumkv  7132  axcaucvg  7849  0tonninf  10382  1tonninf  10383  cbvsum  11310  cbvprod  11508  eirraplem  11726  cnmpt12f  13039  fsumcncntop  13309  dvef  13441  nninfsellemqall  14008  nninfomni  14012  exmidsbthr  14015