Theorem eqtr2i 2251

Description: An equality transitivity inference. (Contributed by NM, 21-Feb-1995.)

Hypotheses

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

Assertion

Ref	Expression
eqtr2i	|- C = A

Proof of Theorem eqtr2i

Step	Hyp	Ref	Expression
1		eqtr2i.1	. . 3 |- A = B
2		eqtr2i.2	. . 3 |- B = C
3	1, 2	eqtri 2250	. 2 |- A = C
4	3	eqcomi 2233	1 |- C = A

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:  3eqtrri  2255  3eqtr2ri  2257  symdif1  3469  dfif3  3616  dfsn2  3680  prprc1  3775  ruv  4642  xpindi  4857  xpindir  4858  dmcnvcnv  4948  rncnvcnv  4949  imainrect  5174  dfrn4  5189  fcoi1  5506  foimacnv  5590  fsnunfv  5840  dfoprab3  6337  fiintim  7093  sbthlemi8  7131  pitonnlem1  8032  ixi  8730  recexaplem2  8799  zeo  9552  num0h  9589  dec10p  9620  fseq1p1m1  10290  cats1fvn  11296  fsumrelem  11982  ef0lem  12171  ef01bndlem  12267  3lcm2e6woprm  12608  strsl0  13081  0g0  13409  tgioo  15228  tgqioo  15229  dveflem  15400  sincos4thpi  15514  coskpi  15522