ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  imaeq2i Unicode version

Theorem imaeq2i 4849
Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008.)
Hypothesis
Ref Expression
imaeq1i.1  |-  A  =  B
Assertion
Ref Expression
imaeq2i  |-  ( C
" A )  =  ( C " B
)

Proof of Theorem imaeq2i
StepHypRef Expression
1 imaeq1i.1 . 2  |-  A  =  B
2 imaeq2 4847 . 2  |-  ( A  =  B  ->  ( C " A )  =  ( C " B
) )
31, 2ax-mp 5 1  |-  ( C
" A )  =  ( C " B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1316   "cima 4512
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-sn 3503  df-pr 3504  df-op 3506  df-br 3900  df-opab 3960  df-xp 4515  df-cnv 4517  df-dm 4519  df-rn 4520  df-res 4521  df-ima 4522
This theorem is referenced by:  cnvimarndm  4873  dmco  5017  fnimapr  5449  ssimaex  5450  imauni  5630  isoini2  5688  uniqs  6455  fiintim  6785  fidcenumlemrks  6809  fidcenumlemr  6811  nn0supp  8997  ennnfonelem1  11847  ennnfonelemhf1o  11853  retopbas  12619
  Copyright terms: Public domain W3C validator