Theorem eqtr2id 2275

Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998.)

Hypotheses

Ref	Expression
eqtr2id.1	|- A = B
eqtr2id.2	|- ( ph -> B = C )

Assertion

Ref	Expression
eqtr2id	|- ( ph -> C = A )

Proof of Theorem eqtr2id

Step	Hyp	Ref	Expression
1		eqtr2id.1	. . 3 |- A = B
2		eqtr2id.2	. . 3 |- ( ph -> B = C )
3	1, 2	eqtrid 2274	. 2 |- ( ph -> A = C )
4	3	eqcomd 2235	1 |- ( ph -> C = A )

Syntax hints:   -> wi 4   = 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:  eqtr3di  2277  opeqsn  4339  dcextest  4673  relop  4872  funopg  5352  funcnvres  5394  mapsnconst  6841  snexxph  7117  apreap  8734  recextlem1  8798  nn0supp  9421  intqfrac2  10541  hashprg  11030  hashfacen  11058  ccatrid  11142  explecnv  12016  grp1inv  13640  rnrhmsubrg  14216  rerestcntop  15232  rerest  15234  mpomulcn  15240  binom4  15653  wlkvtxedg  16074