Theorem xpeq2i 4384

Description: Equality inference for cross product. (Contributed by NM, 21-Dec-2008.)

Hypothesis

Ref	Expression
xpeq1i.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
xpeq2i	⊢ (𝐶 × 𝐴) = (𝐶 × 𝐵)

Proof of Theorem xpeq2i

Step	Hyp	Ref	Expression
1		xpeq1i.1	. 2 ⊢ 𝐴 = 𝐵
2		xpeq2 4378	. 2 ⊢ (𝐴 = 𝐵 → (𝐶 × 𝐴) = (𝐶 × 𝐵))
3	1, 2	ax-mp 7	1 ⊢ (𝐶 × 𝐴) = (𝐶 × 𝐵)

Syntax hints:   = wceq 1284   × cxp 4361

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-opab 3840  df-xp 4369

This theorem is referenced by:  xpindir  4490  xpexgALT  5780  xp1en  6320