Theorem 3brtr3 2642

Description: Substitution of equality into both sides of a binary relation.

Hypotheses

Ref	Expression
3brtr3.1	|- ARB
3brtr3.2	|- A = C
3brtr3.3	|- B = D

Assertion

Ref	Expression
3brtr3	|- CRD

Proof of Theorem 3brtr3

Step	Hyp	Ref	Expression
1		3brtr3.2	. . 3 |- A = C
2		3brtr3.1	. . 3 |- ARB
3	1, 2	eqbrtrr 2636	. 2 |- CRB
4		3brtr3.3	. 2 |- B = D
5	3, 4	breqtr 2638	1 |- CRD

Syntax hints:   = wceq 956   class class class wbr 2619

This theorem is referenced by:  sqrlem11 6683  efaddlem12 7349  ef1tllem 7381  efm1lim 7411  sin01bndlem1 7467  cos01bndlem2 7470  sin01gt0 7476  pilem1 8671  sincos6thpi 8711  projlem5 9190  nmoptri2 10032

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-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-un 2050  df-sn 2412  df-pr 2413  df-op 2416  df-br 2620

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