Theorem imaeq1d 4942

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

Hypothesis

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

Assertion

Ref	Expression
imaeq1d	⊢ (φ → (A “ C) = (B “ C))

Proof of Theorem imaeq1d

Step	Hyp	Ref	Expression
1		imaeq1d.1	. 2 ⊢ (φ → A = B)
2		imaeq1 4938	. 2 ⊢ (A = B → (A “ C) = (B “ C))
3	1, 2	syl 15	1 ⊢ (φ → (A “ C) = (B “ C))

Syntax hints:   → wi 4   = wceq 1642   “ cima 4723

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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-rex 2621  df-br 4641  df-ima 4728

This theorem is referenced by:  imaeq12d  4944  nfimad  4955  foimacnv  5304  enprmaplem3  6079  enprmaplem5  6081  enprmaplem6  6082