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Theorem xpeq2 4360
 Description: Equality theorem for cross product. (Contributed by NM, 5-Jul-1994.)
Assertion
Ref Expression
xpeq2

Proof of Theorem xpeq2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq2 2101 . . . 4
21anbi2d 437 . . 3
32opabbidv 3823 . 2
4 df-xp 4351 . 2
5 df-xp 4351 . 2
63, 4, 53eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243   wcel 1393  copab 3817   cxp 4343 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-opab 3819  df-xp 4351 This theorem is referenced by:  xpeq12  4364  xpeq2i  4366  xpeq2d  4369  xpeq0r  4746  xpdisj2  4748  xpcomeng  6302
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