Theorem bj-xtageq 37011

Description: The products of a given class and the tagging of either of two equal classes are equal. (Contributed by BJ, 6-Apr-2019.)

Assertion

Ref	Expression
bj-xtageq	⊢ (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵))

Proof of Theorem bj-xtageq

Step	Hyp	Ref	Expression
1		bj-tageq 36999	. 2 ⊢ (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵)
2	1	xpeq2d 5689	1 ⊢ (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵))

Syntax hints:   → wi 4   = wceq 1540   × cxp 5657  tag bj-ctag 36997

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-rex 3062  df-v 3466  df-un 3936  df-opab 5187  df-xp 5665  df-bj-sngl 36989  df-bj-tag 36998

This theorem is referenced by:  bj-1upleq  37022  bj-2upleq  37035