Theorem 3eqtrri 2378

Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006.) (Proof shortened by Andrew Salmon, 25-May-2011.)

Hypotheses

Ref	Expression
3eqtri.1	⊢ A = B
3eqtri.2	⊢ B = C
3eqtri.3	⊢ C = D

Assertion

Ref	Expression
3eqtrri	⊢ D = A

Proof of Theorem 3eqtrri

Step	Hyp	Ref	Expression
1		3eqtri.1	. . 3 ⊢ A = B
2		3eqtri.2	. . 3 ⊢ B = C
3	1, 2	eqtri 2373	. 2 ⊢ A = C
4		3eqtri.3	. 2 ⊢ C = D
5	3, 4	eqtr2i 2374	1 ⊢ D = A

Syntax hints:   = wceq 1642

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-cleq 2346

This theorem is referenced by:  dfun4  3547  dfif5  3675  compldif  4070  opeq  4620  mucnc  6132  nnc3n3p2  6280