Theorem eqtr2id 2242

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 2241	. 2 |- ( ph -> A = C )
4	3	eqcomd 2202	1 |- ( ph -> C = A )

Syntax hints:   -> wi 4   = wceq 1364

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 1461  ax-gen 1463  ax-4 1524  ax-17 1540  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-cleq 2189

This theorem is referenced by:  eqtr3di  2244  opeqsn  4286  dcextest  4618  relop  4817  funopg  5293  funcnvres  5332  mapsnconst  6762  snexxph  7025  apreap  8633  recextlem1  8697  nn0supp  9320  intqfrac2  10430  hashprg  10919  hashfacen  10947  explecnv  11689  grp1inv  13311  rnrhmsubrg  13886  rerestcntop  14902  rerest  14904  mpomulcn  14910  binom4  15323