Theorem imaeq2d 4942

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

Hypothesis

Ref	Expression
imaeq1d.1	⊢ (φ → A = B)

Assertion

Ref	Expression
imaeq2d	⊢ (φ → (C “ A) = (C “ B))

Proof of Theorem imaeq2d

Step	Hyp	Ref	Expression
1		imaeq1d.1	. 2 ⊢ (φ → A = B)
2		imaeq2 4938	. 2 ⊢ (A = B → (C “ A) = (C “ B))
3	1, 2	syl 15	1 ⊢ (φ → (C “ A) = (C “ B))

Syntax hints:   → wi 4   = wceq 1642   “ cima 4722

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-ima 4727

This theorem is referenced by:  imaeq12d  4943  nfimad  4954  imasn  5018  fvco2  5382  fsn2  5434  eceq1  5962  uniqs2  5985  mapsn  6026  ncdisjun  6136  sbthlem1  6203