Theorem mpteq2i 4092

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 4091	1 |- ( x e. A |-> B ) = ( x e. A |-> C )

Syntax hints:   = wceq 1353   e. wcel 2148   |-> cmpt 4066

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-ral 2460  df-opab 4067  df-mpt 4068

This theorem is referenced by:  frecsuc  6411  fodjuomni  7150  fodjumkv  7161  axcaucvg  7902  0tonninf  10442  1tonninf  10443  cbvsum  11371  cbvprod  11569  eirraplem  11787  cnmpt12f  13926  fsumcncntop  14196  dvef  14328  nninfsellemqall  14904  nninfomni  14908  exmidsbthr  14911