Theorem bj-1upleq 32987

Description: Substitution property for (| - |). (Contributed by BJ, 6-Apr-2019.)

Assertion

Ref	Expression
bj-1upleq	|- ( A = B -> (| A|) = (| B|) )

Proof of Theorem bj-1upleq

Step	Hyp	Ref	Expression
1		bj-xtageq 32976	. 2 |- ( A = B -> ( { (/) } X. tag A ) = ( { (/) } X. tag B ) )
2		df-bj-1upl 32986	. 2 |- (| A|) = ( { (/) } X. tag A )
3		df-bj-1upl 32986	. 2 |- (| B|) = ( { (/) } X. tag B )
4	1, 2, 3	3eqtr4g 2681	1 |- ( A = B -> (| A|) = (| B|) )

Syntax hints:   -> wi 4   = wceq 1483   (/)c0 3915   {csn 4177   X. cxp 5112  tag bj-ctag 32962  (|bj-c1upl 32985

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rex 2918  df-v 3202  df-un 3579  df-opab 4713  df-xp 5120  df-bj-sngl 32954  df-bj-tag 32963  df-bj-1upl 32986

This theorem is referenced by:  bj-1uplth  32995  bj-2upleq  33000