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Theorem imaeq1i 4885
Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008.)
Hypothesis
Ref Expression
imaeq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
imaeq1i (𝐴𝐶) = (𝐵𝐶)

Proof of Theorem imaeq1i
StepHypRef Expression
1 imaeq1i.1 . 2 𝐴 = 𝐵
2 imaeq1 4883 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
31, 2ax-mp 5 1 (𝐴𝐶) = (𝐵𝐶)
Colors of variables: wff set class
Syntax hints:   = wceq 1332  cima 4549
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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3079  df-in 3081  df-ss 3088  df-sn 3537  df-pr 3538  df-op 3540  df-br 3937  df-opab 3997  df-cnv 4554  df-dm 4556  df-rn 4557  df-res 4558  df-ima 4559
This theorem is referenced by:  mptpreima  5039  isarep2  5217  infrenegsupex  9415  infxrnegsupex  11063  ssidcn  12416  cnco  12427
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