Theorem 3eqtr4ri 2120

Description: An inference from three chained equalities. (Contributed by NM, 2-Sep-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.)

Hypotheses

Ref	Expression
3eqtr4i.1	|- A = B
3eqtr4i.2	|- C = A
3eqtr4i.3	|- D = B

Assertion

Ref	Expression
3eqtr4ri	|- D = C

Proof of Theorem 3eqtr4ri

Step	Hyp	Ref	Expression
1		3eqtr4i.3	. . 3 |- D = B
2		3eqtr4i.1	. . 3 |- A = B
3	1, 2	eqtr4i 2112	. 2 |- D = A
4		3eqtr4i.2	. 2 |- C = A
5	3, 4	eqtr4i 2112	1 |- D = C

Syntax hints:   = wceq 1290

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-4 1446  ax-17 1465  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-cleq 2082

This theorem is referenced by:  cbvreucsf  2993  dfif6  3399  qdass  3543  tpidm12  3545  unipr  3673  dfdm4  4641  dmun  4656  resres  4738  inres  4743  resdifcom  4744  resiun1  4745  imainrect  4889  coundi  4945  coundir  4946  funopg  5061  offres  5920  mpt2mptsx  5981  cnvoprab  6013  snec  6367  halfpm6th  8697  numsucc  8977  decbin2  9078  fsumadd  10861  fsum2d  10890  znnen  11550