Theorem eqtr2id 2250

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 2249	. 2 |- ( ph -> A = C )
4	3	eqcomd 2210	1 |- ( ph -> C = A )

Syntax hints:   -> wi 4   = wceq 1372

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 1469  ax-gen 1471  ax-4 1532  ax-17 1548  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-cleq 2197

This theorem is referenced by:  eqtr3di  2252  opeqsn  4296  dcextest  4628  relop  4827  funopg  5304  funcnvres  5346  mapsnconst  6780  snexxph  7051  apreap  8659  recextlem1  8723  nn0supp  9346  intqfrac2  10462  hashprg  10951  hashfacen  10979  ccatrid  11061  explecnv  11787  grp1inv  13410  rnrhmsubrg  13985  rerestcntop  15001  rerest  15003  mpomulcn  15009  binom4  15422