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Theorem imaeq2i 4879
Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008.)
Hypothesis
Ref Expression
imaeq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
imaeq2i (𝐶𝐴) = (𝐶𝐵)

Proof of Theorem imaeq2i
StepHypRef Expression
1 imaeq1i.1 . 2 𝐴 = 𝐵
2 imaeq2 4877 . 2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
31, 2ax-mp 5 1 (𝐶𝐴) = (𝐶𝐵)
Colors of variables: wff set class
Syntax hints:   = wceq 1331  cima 4542
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 2121
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-opab 3990  df-xp 4545  df-cnv 4547  df-dm 4549  df-rn 4550  df-res 4551  df-ima 4552
This theorem is referenced by:  cnvimarndm  4903  dmco  5047  fnimapr  5481  ssimaex  5482  imauni  5662  isoini2  5720  uniqs  6487  fiintim  6817  fidcenumlemrks  6841  fidcenumlemr  6843  nn0supp  9036  ennnfonelem1  11927  ennnfonelemhf1o  11933  retopbas  12702
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