NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  imaeq2i GIF version

Theorem imaeq2i 4940
Description: Equality theorem for image. (Contributed by set.mm contributors, 21-Dec-2008.)
Hypothesis
Ref Expression
imaeq1i.1 A = B
Assertion
Ref Expression
imaeq2i (CA) = (CB)

Proof of Theorem imaeq2i
StepHypRef Expression
1 imaeq1i.1 . 2 A = B
2 imaeq2 4938 . 2 (A = B → (CA) = (CB))
31, 2ax-mp 5 1 (CA) = (CB)
Colors of variables: wff setvar class
Syntax hints:   = 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:  elima1c  4947  cnvimarndm  5017  dmco  5089  imain  5172  fnimapr  5374  imauni  5465  isoini2  5498  uniqs  5984
  Copyright terms: Public domain W3C validator