Theorem bj-xtageq 36954

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 36942	. 2 ⊢ (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵)
2	1	xpeq2d 5730	1 ⊢ (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵))

Syntax hints:   → wi 4   = wceq 1537   × cxp 5698  tag bj-ctag 36940

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rex 3077  df-v 3490  df-un 3981  df-opab 5229  df-xp 5706  df-bj-sngl 36932  df-bj-tag 36941

This theorem is referenced by:  bj-1upleq  36965  bj-2upleq  36978