Theorem imaeq1d 3399

Description: Equality theorem for image. (Contributed by FL, 15-Dec-2006.)

Hypothesis

Ref	Expression
imaeq1d.1	|- (ph -> A = B)

Assertion

Ref	Expression
imaeq1d	|- (ph -> (A"C) = (B"C))

Proof of Theorem imaeq1d

Step	Hyp	Ref	Expression
1		imaeq1d.1	. 2 |- (ph -> A = B)
2		imaeq1 3397	. 2 |- (A = B -> (A"C) = (B"C))
3	1, 2	syl 10	1 |- (ph -> (A"C) = (B"C))

Syntax hints:   -> wi 3   = wceq 955  "cima 3169

This theorem is referenced by:  hbimad 3408  csbima12g 3409  ssenen 4493  iscn 7718  idcn 7726  ishomeo 10463  idhme 10468  cnvhmpha 10471  cnvhmphb 10472  cnvhmph 10473  hmphsyma 10474

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-11 966  ax-12 967  ax-13 968  ax-14 969  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1209  ax-11o 1217  ax-ext 1458  ax-sep 2699  ax-pow 2738  ax-pr 2775

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 980  df-sb 1171  df-eu 1381  df-mo 1382  df-clab 1463  df-cleq 1468  df-clel 1471  df-ne 1585  df-v 1809  df-dif 2046  df-un 2047  df-in 2048  df-ss 2050  df-nul 2278  df-pw 2399  df-sn 2409  df-pr 2410  df-op 2413  df-br 2616  df-opab 2663  df-cnv 3182  df-dm 3184  df-rn 3185  df-res 3186  df-ima 3187

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