Theorem mpteq2i 4199

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 4198	1 |- ( x e. A |-> B ) = ( x e. A |-> C )

Syntax hints:   = wceq 1398   e. wcel 2205   |-> cmpt 4173

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-ral 2527  df-opab 4174  df-mpt 4175

This theorem is referenced by:  frecsuc  6640  fodjuomni  7442  fodjumkv  7453  axcaucvg  8217  0tonninf  10806  1tonninf  10807  cbvsum  12049  cbvprod  12248  eirraplem  12467  ballotfilemfc0  13153  ballotfilemfcc  13154  znzrh2  14811  cnmpt12f  15168  fsumcncntop  15449  dvmptfsum  15607  dvef  15609  plyco  15641  plycj  15643  nninfsellemqall  16810  nninfomni  16814  nnnninfex  16817  exmidsbthr  16820