Theorem imaeq1i 4940

Description: Equality theorem for image. (Contributed by set.mm contributors, 21-Dec-2008.)

Hypothesis

Ref	Expression
imaeq1i.1	⊢ A = B

Assertion

Ref	Expression
imaeq1i	⊢ (A “ C) = (B “ C)

Proof of Theorem imaeq1i

Step	Hyp	Ref	Expression
1		imaeq1i.1	. 2 ⊢ A = B
2		imaeq1 4938	. 2 ⊢ (A = B → (A “ C) = (B “ C))
3	1, 2	ax-mp 5	1 ⊢ (A “ C) = (B “ C)

Syntax hints:   = 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:  mptpreima  5683