Theorem imaeq2i 4767

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

Step	Hyp	Ref	Expression
1		imaeq1i.1	. 2 ⊢ 𝐴 = 𝐵
2		imaeq2 4765	. 2 ⊢ (𝐴 = 𝐵 → (𝐶 “ 𝐴) = (𝐶 “ 𝐵))
3	1, 2	ax-mp 7	1 ⊢ (𝐶 “ 𝐴) = (𝐶 “ 𝐵)

Syntax hints:   = wceq 1289   “ cima 4439

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3003  df-in 3005  df-ss 3012  df-sn 3450  df-pr 3451  df-op 3453  df-br 3844  df-opab 3898  df-xp 4442  df-cnv 4444  df-dm 4446  df-rn 4447  df-res 4448  df-ima 4449

This theorem is referenced by:  cnvimarndm  4791  dmco  4934  fnimapr  5358  ssimaex  5359  imauni  5532  isoini2  5590  uniqs  6340  fiintim  6629  fidcenumlemrks  6652  fidcenumlemr  6654  nn0supp  8715