Theorem syl6eqbrr 2658

Description: A chained equality inference for a binary relation.

Hypotheses

Ref	Expression
syl6eqbrr.1	|- (ph -> B = A)
syl6eqbrr.2	|- BRC

Assertion

Ref	Expression
syl6eqbrr	|- (ph -> ARC)

Proof of Theorem syl6eqbrr

Step	Hyp	Ref	Expression
1		syl6eqbrr.1	. . 3 |- (ph -> B = A)
2	1	eqcomd 1483	. 2 |- (ph -> A = B)
3		syl6eqbrr.2	. 2 |- BRC
4	2, 3	syl6eqbr 2657	1 |- (ph -> ARC)

Syntax hints:   -> wi 3   = wceq 958   class class class wbr 2624

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-un 2053  df-sn 2416  df-pr 2417  df-op 2420  df-br 2625

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