Theorem 3eqtr2i 2379

Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006.)

Hypotheses

Ref	Expression
3eqtr2i.1	⊢ A = B
3eqtr2i.2	⊢ C = B
3eqtr2i.3	⊢ C = D

Assertion

Ref	Expression
3eqtr2i	⊢ A = D

Proof of Theorem 3eqtr2i

Step	Hyp	Ref	Expression
1		3eqtr2i.1	. . 3 ⊢ A = B
2		3eqtr2i.2	. . 3 ⊢ C = B
3	1, 2	eqtr4i 2376	. 2 ⊢ A = C
4		3eqtr2i.3	. 2 ⊢ C = D
5	3, 4	eqtri 2373	1 ⊢ A = D

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:  indif  3498  dfrab3  3532  iunid  4022  inindif  4076  fnpm  6009