Theorem syl5breq 3372

Description: A chained equality inference for a binary relation.

Hypotheses

Ref	Expression
syl5breq.1	|- (ph -> A = B)
syl5breq.2	|- CRA

Assertion

Ref	Expression
syl5breq	|- (ph -> CRB)

Proof of Theorem syl5breq

Step	Hyp	Ref	Expression
1		syl5breq.2	. . 3 |- CRA
2	1	a1i 8	. 2 |- (ph -> CRA)
3		syl5breq.1	. 2 |- (ph -> A = B)
4	2, 3	breqtrd 3361	1 |- (ph -> CRB)

Syntax hints:   -> wi 3   = wceq 1298   class class class wbr 3338

This theorem is referenced by:  syl5breqr 3373  phplem3 5604  sqrge0i 7952  blocnilem 9804  siilem1 9852  nmcoplbi 11595  nmbdfnlbi 11615  nmcfnlbi 11624  unierri 11674  leoprf2 11698  leoprf 11699

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-9 1307  ax-10 1308  ax-11 1309  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-or 241  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-v 2294  df-un 2600  df-sn 3049  df-pr 3050  df-op 3053  df-br 3339

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