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Theorem imaeq2d 4611
Description: Equality theorem for image. (Contributed by FL, 15-Dec-2006.)
Hypothesis
Ref Expression
imaeq1d.1 (φA = B)
Assertion
Ref Expression
imaeq2d (φ → (𝐶A) = (𝐶B))

Proof of Theorem imaeq2d
StepHypRef Expression
1 imaeq1d.1 . 2 (φA = B)
2 imaeq2 4607 . 2 (A = B → (𝐶A) = (𝐶B))
31, 2syl 14 1 (φ → (𝐶A) = (𝐶B))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  cima 4291
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-xp 4294  df-cnv 4296  df-dm 4298  df-rn 4299  df-res 4300  df-ima 4301
This theorem is referenced by:  imaeq12d  4612  nfimad  4620  elimasng  4636  ressn  4801  foima  5054  f1imacnv  5086  fvco2  5185  fsn2  5280  resfunexg  5325  funfvima3  5335  funiunfvdm  5345  isoselem  5402  fnexALT  5682  eceq1  6077  uniqs2  6102  ecinxp  6117
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