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Theorem mpteq2dva 3903
Description: Slightly more general equality inference for the maps-to notation. (Contributed by Scott Fenton, 25-Apr-2012.)
Hypothesis
Ref Expression
mpteq2dva.1  |-  ( (
ph  /\  x  e.  A )  ->  B  =  C )
Assertion
Ref Expression
mpteq2dva  |-  ( ph  ->  ( x  e.  A  |->  B )  =  ( x  e.  A  |->  C ) )
Distinct variable group:    ph, x
Allowed substitution hints:    A( x)    B( x)    C( x)

Proof of Theorem mpteq2dva
StepHypRef Expression
1 nfv 1464 . 2  |-  F/ x ph
2 mpteq2dva.1 . 2  |-  ( (
ph  /\  x  e.  A )  ->  B  =  C )
31, 2mpteq2da 3902 1  |-  ( ph  ->  ( x  e.  A  |->  B )  =  ( x  e.  A  |->  C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    = wceq 1287    e. wcel 1436    |-> cmpt 3874
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-ral 2360  df-opab 3875  df-mpt 3876
This theorem is referenced by:  mpteq2dv  3904  fmptapd  5451  offval  5820  offval2  5827  caofinvl  5834  caofcom  5835  freceq1  6111  freceq2  6112  mapxpen  6516  xpmapenlem  6517  fser0const  9850  sumeq1  10636  sumeq2  10640
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