Theorem 3eqtr3ri 2069

Description: An inference from three chained equalities. (Contributed by NM, 15-Aug-2004.)

Hypotheses

Ref	Expression
3eqtr3i.1	|- A = B
3eqtr3i.2	|- A = C
3eqtr3i.3	|- B = D

Assertion

Ref	Expression
3eqtr3ri	|- D = C

Proof of Theorem 3eqtr3ri

Step	Hyp	Ref	Expression
1		3eqtr3i.3	. 2 |- B = D
2		3eqtr3i.1	. . 3 |- A = B
3		3eqtr3i.2	. . 3 |- A = C
4	2, 3	eqtr3i 2062	. 2 |- B = C
5	1, 4	eqtr3i 2062	1 |- D = C

Syntax hints:   = wceq 1243

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-cleq 2033

This theorem is referenced by:  indif2  3181  resdm2  4811  co01  4835  1mhlfehlf  8143  rei  9499  resqrexlemover  9608