Theorem syl5ssr 2106

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 1479	. 2 |- C = A
4	1, 3	syl5ss 2105	1 |- (ph -> C (_ B)

Syntax hints:   -> wi 3   = wceq 956   (_ wss 2047

This theorem is referenced by:  unixp0 3518  fimacnvdisj 3649  fimacnv 3810  dmen 4407  rankelun 4707  cardprc 4861  alephgeom 4882  chssoct 9419

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-in 2051  df-ss 2053

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