Theorem mpteq2i 4148

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 4147	1 |- ( x e. A |-> B ) = ( x e. A |-> C )

Syntax hints:   = wceq 1373   e. wcel 2178   |-> cmpt 4122

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 4123  df-mpt 4124

This theorem is referenced by:  frecsuc  6518  fodjuomni  7279  fodjumkv  7290  axcaucvg  8050  0tonninf  10624  1tonninf  10625  cbvsum  11832  cbvprod  12030  eirraplem  12249  znzrh2  14569  cnmpt12f  14919  fsumcncntop  15200  dvmptfsum  15358  dvef  15360  plyco  15392  plycj  15394  nninfsellemqall  16262  nninfomni  16266  nnnninfex  16269  exmidsbthr  16272