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Theorem xpeq1d 4311
Description: Equality deduction for cross product. (Contributed by Jeff Madsen, 17-Jun-2010.)
Hypothesis
Ref Expression
xpeq1d.1 (φA = B)
Assertion
Ref Expression
xpeq1d (φ → (A × 𝐶) = (B × 𝐶))

Proof of Theorem xpeq1d
StepHypRef Expression
1 xpeq1d.1 . 2 (φA = B)
2 xpeq1 4302 . 2 (A = B → (A × 𝐶) = (B × 𝐶))
31, 2syl 14 1 (φ → (A × 𝐶) = (B × 𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242   × cxp 4286
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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-opab 3810  df-xp 4294
This theorem is referenced by:  xpssres  4588
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