 New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  symdifeq2i GIF version

Theorem symdifeq2i 3252
 Description: Equality inference for symmetric difference. (Contributed by SF, 11-Jan-2015.)
Hypothesis
Ref Expression
symdifeqi.1 A = B
Assertion
Ref Expression
symdifeq2i (CA) = (CB)

Proof of Theorem symdifeq2i
StepHypRef Expression
1 symdifeqi.1 . 2 A = B
2 symdifeq2 3249 . 2 (A = B → (CA) = (CB))
31, 2ax-mp 8 1 (CA) = (CB)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ⊕ csymdif 3209 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-nan 1288  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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-symdif 3216 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator