Theorem bj-xtageq 37191

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 37179	. 2 ⊢ (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵)
2	1	xpeq2d 5655	1 ⊢ (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵))

Syntax hints:   → wi 4   = wceq 1542   × cxp 5623  tag bj-ctag 37177

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rex 3062  df-v 3443  df-un 3907  df-opab 5162  df-xp 5631  df-bj-sngl 37169  df-bj-tag 37178

This theorem is referenced by:  bj-1upleq  37202  bj-2upleq  37215