Theorem syl5ssr 2096

Description: A chained subclass and equality deduction.

Hypotheses

Ref	Expression
syl5ssr.1	|- (ph -> A (_ B)
syl5ssr.2	|- A = C

Assertion

Ref	Expression
syl5ssr	|- (ph -> C (_ B)

Proof of Theorem syl5ssr

Step	Hyp	Ref	Expression
1		syl5ssr.1	. 2 |- (ph -> A (_ B)
2		syl5ssr.2	. . 3 |- A = C
3	2	eqcomi 1471	. 2 |- C = A
4	1, 3	syl5ss 2095	1 |- (ph -> C (_ B)

Syntax hints:   -> wi 3   = wceq 953   (_ wss 2037

This theorem is referenced by:  unixp0 3504  fimacnvdisj 3634  fimacnv 3795  dmen 4388  rankelun 4679  cardprc 4833  alephgeom 4854  chssoct 9334

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-in 2041  df-ss 2043

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