Theorem bj-tageq 32964

Description: Substitution property for tag. (Contributed by BJ, 6-Oct-2018.)

Assertion

Ref	Expression
bj-tageq	|- ( A = B -> tag A = tag B )

Proof of Theorem bj-tageq

Step	Hyp	Ref	Expression
1		bj-sngleq 32955	. . 3 |- ( A = B -> sngl A = sngl B )
2	1	uneq1d 3766	. 2 |- ( A = B -> (sngl A u. { (/) } ) = (sngl B u. { (/) } ) )
3		df-bj-tag 32963	. 2 |- tag A = (sngl A u. { (/) } )
4		df-bj-tag 32963	. 2 |- tag B = (sngl B u. { (/) } )
5	2, 3, 4	3eqtr4g 2681	1 |- ( A = B -> tag A = tag B )

Syntax hints:   -> wi 4   = wceq 1483   u. cun 3572   (/)c0 3915   {csn 4177  sngl bj-csngl 32953  tag bj-ctag 32962

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-bj-sngl 32954  df-bj-tag 32963

This theorem is referenced by:  bj-xtageq  32976