Theorem imaeq2d 3401

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

Hypothesis

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

Assertion

Ref	Expression
imaeq2d	|- (ph -> (C"A) = (C"B))

Proof of Theorem imaeq2d

Step	Hyp	Ref	Expression
1		imaeq1d.1	. 2 |- (ph -> A = B)
2		imaeq2 3399	. 2 |- (A = B -> (C"A) = (C"B))
3	1, 2	syl 10	1 |- (ph -> (C"A) = (C"B))

Syntax hints:   -> wi 3   = wceq 955  "cima 3170

This theorem is referenced by:  hbimad 3409  csbima12g 3410  elimasng 3424  eliniseg 3426  fnex 3604  fveq2 3721  fsn2 3833  funfvima3 3851  isofrlem 3898  curry1 4095  eceq2 4275  mapsn 4342  cnconst 7759  metcnp 7870

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 1210  ax-11o 1218  ax-ext 1459  ax-sep 2700  ax-pow 2739  ax-pr 2776

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 980  df-sb 1172  df-eu 1382  df-mo 1383  df-clab 1464  df-cleq 1469  df-clel 1472  df-ne 1586  df-v 1810  df-dif 2047  df-un 2048  df-in 2049  df-ss 2051  df-nul 2279  df-pw 2400  df-sn 2410  df-pr 2411  df-op 2414  df-br 2617  df-opab 2664  df-xp 3181  df-cnv 3183  df-dm 3185  df-rn 3186  df-res 3187  df-ima 3188

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