Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  funeqd Unicode version

Theorem funeqd 5140
 Description: Equality deduction for the function predicate. (Contributed by NM, 23-Feb-2013.)
Hypothesis
Ref Expression
funeqd.1
Assertion
Ref Expression
funeqd

Proof of Theorem funeqd
StepHypRef Expression
1 funeqd.1 . 2
2 funeq 5138 . 2
31, 2syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1331   wfun 5112 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-in 3072  df-ss 3079  df-br 3925  df-opab 3985  df-rel 4541  df-cnv 4542  df-co 4543  df-fun 5120 This theorem is referenced by:  funopg  5152  funsng  5164  funcnvuni  5187  f1eq1  5318  frecuzrdgtclt  10187  shftfn  10589  ennnfonelemfun  11919  ennnfonelemf1  11920  isstruct2im  11958  isstruct2r  11959  structfung  11965  setsfun  11983  setsfun0  11984
 Copyright terms: Public domain W3C validator