Theorem 3eqtr2i 2232

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 2229	. 2 |- A = C
4		3eqtr2i.3	. 2 |- C = D
5	3, 4	eqtri 2226	1 |- A = D

Syntax hints:   = wceq 1373

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 1470  ax-gen 1472  ax-4 1533  ax-17 1549  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-cleq 2198

This theorem is referenced by:  dfrab3  3449  iunid  3983  cnvcnv  5135  cocnvcnv2  5194  fmptap  5774  exmidfodomrlemim  7309  negdii  8356  halfpm6th  9257  numma  9547  numaddc  9551  6p5lem  9573  8p2e10  9583  binom2i  10793  0.999...  11832  flodddiv4  12247  6gcd4e2  12316  dfphi2  12542  karatsuba  12753  cosq23lt0  15305  pigt3  15316  1sgm2ppw  15467  2lgsoddprmlem3c  15586  2lgsoddprmlem3d  15587  nninfomni  15956