Theorem eqtr2id 2223

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 2222	. 2 |- ( ph -> A = C )
4	3	eqcomd 2183	1 |- ( ph -> C = A )

Syntax hints:   -> wi 4   = wceq 1353

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 1447  ax-gen 1449  ax-4 1510  ax-17 1526  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-cleq 2170

This theorem is referenced by:  eqtr3di  2225  opeqsn  4253  dcextest  4581  relop  4778  funopg  5251  funcnvres  5290  mapsnconst  6694  snexxph  6949  apreap  8544  recextlem1  8608  nn0supp  9228  intqfrac2  10319  hashprg  10788  hashfacen  10816  explecnv  11513  grp1inv  12977  rerestcntop  14053  binom4  14400