Theorem 3eqtr3ri 2382

Description: An inference from three chained equalities. (Contributed by NM, 15-Aug-2004.)

Hypotheses

Ref	Expression
3eqtr3i.1	⊢ A = B
3eqtr3i.2	⊢ A = C
3eqtr3i.3	⊢ B = D

Assertion

Ref	Expression
3eqtr3ri	⊢ D = C

Proof of Theorem 3eqtr3ri

Step	Hyp	Ref	Expression
1		3eqtr3i.3	. 2 ⊢ B = D
2		3eqtr3i.1	. . 3 ⊢ A = B
3		3eqtr3i.2	. . 3 ⊢ A = C
4	2, 3	eqtr3i 2375	. 2 ⊢ B = C
5	1, 4	eqtr3i 2375	1 ⊢ D = C

Syntax hints:   = wceq 1642

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-cleq 2346

This theorem is referenced by:  indif2  3499  dfif5  3675  nchoicelem2  6291