Theorem s1eqd 11196

Description: Equality theorem for a singleton word. (Contributed by Mario Carneiro, 26-Feb-2016.)

Hypothesis

Ref	Expression
s1eqd.1	|- ( ph -> A = B )

Assertion

Ref	Expression
s1eqd	|- ( ph -> <" A "> = <" B "> )

Proof of Theorem s1eqd

Step	Hyp	Ref	Expression
1		s1eqd.1	. 2 |- ( ph -> A = B )
2		s1eq 11195	. 2 |- ( A = B -> <" A "> = <" B "> )
3	1, 2	syl 14	1 |- ( ph -> <" A "> = <" B "> )

Syntax hints:   -> wi 4   = wceq 1397   <"cs1 11191

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-3an 1006  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-rex 2516  df-v 2804  df-un 3204  df-sn 3675  df-pr 3676  df-op 3678  df-uni 3894  df-br 4089  df-iota 5286  df-fv 5334  df-s1 11192

This theorem is referenced by:  ccat1st1st  11217  swrds1  11248  swrdlsw  11249  reuccatpfxs1lem  11326  s2eqd  11350  s3eqd  11351  s4eqd  11352  s5eqd  11353  s6eqd  11354  s7eqd  11355  s8eqd  11356