Theorem 3eqtr2i 2066

Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006.)

Hypotheses

Ref	Expression
3eqtr2i.1	|- A = B
3eqtr2i.2	|- C = B
3eqtr2i.3	|- C = D

Assertion

Ref	Expression
3eqtr2i	|- A = D

Proof of Theorem 3eqtr2i

Step	Hyp	Ref	Expression
1		3eqtr2i.1	. . 3 |- A = B
2		3eqtr2i.2	. . 3 |- C = B
3	1, 2	eqtr4i 2063	. 2 |- A = C
4		3eqtr2i.3	. 2 |- C = D
5	3, 4	eqtri 2060	1 |- A = D

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:  dfrab3  3213  iunid  3712  cnvcnv  4773  cocnvcnv2  4832  fmptap  5353  negdii  7295  halfpm6th  8145  numma  8398  numaddc  8402  6p5lem  8416  binom2i  9360