Theorem bj-xtageq 38078

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 38066	. 2 ⊢ (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵)
2	1	xpeq2d 5685	1 ⊢ (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵))

This proof depends on syntax axioms:   → wi 4   = wceq 1570   × cxp 5653  tag bj-ctag 38064

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rex 3091  df-v 3456  df-un 4154  df-opab 5171  df-xp 5661  df-bj-sngl 38056  df-bj-tag 38065

This theorem is used by:  bj-1upleq  38089  bj-2upleq  38102