New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  xpeq2d GIF version

Theorem xpeq2d 4808
 Description: Equality deduction for cross product. (Contributed by Jeff Madsen, 17-Jun-2010.)
Hypothesis
Ref Expression
xpeq1d.1 (φA = B)
Assertion
Ref Expression
xpeq2d (φ → (C × A) = (C × B))

Proof of Theorem xpeq2d
StepHypRef Expression
1 xpeq1d.1 . 2 (φA = B)
2 xpeq2 4799 . 2 (A = B → (C × A) = (C × B))
31, 2syl 15 1 (φ → (C × A) = (C × B))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   × cxp 4770 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-opab 4623  df-xp 4784 This theorem is referenced by:  csbresg  4976  fconstg  5251  fconst5  5455  xpsneng  6050  frecxp  6314  frecxpg  6315
 Copyright terms: Public domain W3C validator