Theorem bj-xtageq 37356

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 37344	. 2 ⊢ (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵)
2	1	xpeq2d 5651	1 ⊢ (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵))

Syntax hints:   → wi 4   = wceq 1548   × cxp 5619  tag bj-ctag 37342

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975  ax-7 2016  ax-8 2123  ax-9 2131  ax-ext 2713

This theorem depends on definitions:  df-bi 209  df-an 398  df-or 855  df-tru 1551  df-ex 1788  df-sb 2075  df-clab 2720  df-cleq 2733  df-clel 2816  df-rex 3066  df-v 3435  df-un 3890  df-opab 5138  df-xp 5627  df-bj-sngl 37334  df-bj-tag 37343

This theorem is referenced by:  bj-1upleq  37367  bj-2upleq  37380