Theorem mpteq2i 4220

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 4219	1 |- ( x e. A |-> B ) = ( x e. A |-> C )

This proof depends on syntax axioms:   = wceq 1402   e. wcel 2209   |-> cmpt 4193

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-ral 2533  df-opab 4194  df-mpt 4195

This theorem is used by:  frecsuc  6683  fodjuomni  7495  fodjumkv  7506  axcaucvg  8273  0tonninf  10897  1tonninf  10898  cbvsum  12150  cbvprod  12349  eirraplem  12568  ballotfilemfc0  13289  ballotfilemfcc  13290  ballotfi  13339  znzrh2  15089  cnmpt12f  15529  fsumcncntop  15810  dvmptfsum  15968  dvef  15970  plyco  16002  plycj  16004  nninfsellemqall  17281  nninfomni  17285  nnnninfex  17288  exmidsbthr  17291