Theorem mpteq2i 4181

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 4180	1 |- ( x e. A |-> B ) = ( x e. A |-> C )

Syntax hints:   = wceq 1398   e. wcel 2202   |-> cmpt 4155

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 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-ral 2516  df-opab 4156  df-mpt 4157

This theorem is referenced by:  frecsuc  6616  fodjuomni  7408  fodjumkv  7419  axcaucvg  8180  0tonninf  10765  1tonninf  10766  cbvsum  12000  cbvprod  12199  eirraplem  12418  znzrh2  14742  cnmpt12f  15097  fsumcncntop  15378  dvmptfsum  15536  dvef  15538  plyco  15570  plycj  15572  nninfsellemqall  16741  nninfomni  16745  nnnninfex  16748  exmidsbthr  16751