Theorem eqtr2id 2251

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 2250	. 2 |- ( ph -> A = C )
4	3	eqcomd 2211	1 |- ( ph -> C = A )

Syntax hints:   -> wi 4   = 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:  eqtr3di  2253  opeqsn  4297  dcextest  4629  relop  4828  funopg  5305  funcnvres  5347  mapsnconst  6781  snexxph  7052  apreap  8660  recextlem1  8724  nn0supp  9347  intqfrac2  10464  hashprg  10953  hashfacen  10981  ccatrid  11063  explecnv  11816  grp1inv  13439  rnrhmsubrg  14014  rerestcntop  15030  rerest  15032  mpomulcn  15038  binom4  15451