Theorem bj-tagci 32972

Description: Characterization of the elements of B in terms of elements of its tagged version. (Contributed by BJ, 6-Oct-2018.)

Assertion

Ref	Expression
bj-tagci	|- ( A e. B -> { A } e. tag B )

Proof of Theorem bj-tagci

Step	Hyp	Ref	Expression
1		bj-snglc 32957	. 2 |- ( A e. B <-> { A } e. sngl B )
2		bj-sngltagi 32970	. 2 |- ( { A } e. sngl B -> { A } e. tag B )
3	1, 2	sylbi 207	1 |- ( A e. B -> { A } e. tag B )

Syntax hints:   -> wi 4   e. wcel 1990   {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  ax-sep 4781  ax-nul 4789  ax-pr 4906

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-ral 2917  df-rex 2918  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-sn 4178  df-pr 4180  df-bj-sngl 32954  df-bj-tag 32963

This theorem is referenced by: (None)