Theorem 3eqtr2i 2256

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 2253	. 2 |- A = C
4		3eqtr2i.3	. 2 |- C = D
5	3, 4	eqtri 2250	1 |- A = D

Syntax hints:   = wceq 1395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1493  ax-gen 1495  ax-4 1556  ax-17 1572  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-cleq 2222

This theorem is referenced by:  dfrab3  3480  iunid  4021  cnvcnv  5181  cocnvcnv2  5240  fmptap  5833  exmidfodomrlemim  7390  negdii  8441  halfpm6th  9342  numma  9632  numaddc  9636  6p5lem  9658  8p2e10  9668  binom2i  10882  0.999...  12048  flodddiv4  12463  6gcd4e2  12532  dfphi2  12758  karatsuba  12969  cosq23lt0  15523  pigt3  15534  1sgm2ppw  15685  2lgsoddprmlem3c  15804  2lgsoddprmlem3d  15805  nninfomni  16473