Theorem syl5eqbrr 2639

Description: A chained equality inference for a binary relation.

Hypotheses

Ref	Expression
syl5eqbrr.1	|- (ph -> ARB)
syl5eqbrr.2	|- A = C

Assertion

Ref	Expression
syl5eqbrr	|- (ph -> CRB)

Proof of Theorem syl5eqbrr

Step	Hyp	Ref	Expression
1		syl5eqbrr.1	. 2 |- (ph -> ARB)
2		syl5eqbrr.2	. 2 |- A = C
3		eqid 1468	. 2 |- B = B
4	1, 2, 3	3brtr3g 2636	1 |- (ph -> CRB)

Syntax hints:   -> wi 3   = wceq 953   class class class wbr 2609

This theorem is referenced by:  undom 4418  iunfi 4543  reclem3pr 5130  nnleltp1t 5901  facwordit 6881  geoisum 7177  geoisum1 7179  ivthlem1 7216  eflt 7347  efcnlem1 7359  infdif 7511

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-or 224  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-v 1803  df-un 2040  df-sn 2402  df-pr 2403  df-op 2406  df-br 2610

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