Theorem s3eq2 11462

Description: Equality theorem for a length 3 word for the second symbol. (Contributed by AV, 4-Jan-2022.)

Assertion

Ref	Expression
s3eq2	|- ( B = D -> <" A B C "> = <" A D C "> )

Proof of Theorem s3eq2

Step	Hyp	Ref	Expression
1		eqidd 2233	. 2 |- ( B = D -> A = A )
2		id 19	. 2 |- ( B = D -> B = D )
3		eqidd 2233	. 2 |- ( B = D -> C = C )
4	1, 2, 3	s3eqd 11456	1 |- ( B = D -> <" A B C "> = <" A D C "> )

Syntax hints:   -> wi 4   = wceq 1398   <"cs3 11435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-rex 2526  df-v 2814  df-un 3214  df-sn 3694  df-pr 3695  df-op 3697  df-uni 3914  df-br 4109  df-iota 5311  df-fv 5359  df-ov 6052  df-s1 11297  df-s2 11441  df-s3 11442

This theorem is referenced by: (None)