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  5829  exmidfodomrlemim  7379  negdii  8430  halfpm6th  9331  numma  9621  numaddc  9625  6p5lem  9647  8p2e10  9657  binom2i  10870  0.999...  12032  flodddiv4  12447  6gcd4e2  12516  dfphi2  12742  karatsuba  12953  cosq23lt0  15507  pigt3  15518  1sgm2ppw  15669  2lgsoddprmlem3c  15788  2lgsoddprmlem3d  15789  nninfomni  16385