Theorem mpteq2i 4147

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 4146	1 |- ( x e. A |-> B ) = ( x e. A |-> C )

Syntax hints:   = wceq 1373   e. wcel 2178   |-> cmpt 4121

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-ral 2491  df-opab 4122  df-mpt 4123

This theorem is referenced by:  frecsuc  6516  fodjuomni  7277  fodjumkv  7288  axcaucvg  8048  0tonninf  10622  1tonninf  10623  cbvsum  11786  cbvprod  11984  eirraplem  12203  znzrh2  14523  cnmpt12f  14873  fsumcncntop  15154  dvmptfsum  15312  dvef  15314  plyco  15346  plycj  15348  nninfsellemqall  16154  nninfomni  16158  nnnninfex  16161  exmidsbthr  16164