Theorem 3eqtr3r 1125

Description: An inference from three chained equalities.

Hypotheses

Ref	Expression
3eqtr3.1	⊢ A = B
3eqtr3.2	⊢ A = C
3eqtr3.3	⊢ B = D

Assertion

Ref	Expression
3eqtr3r	⊢ D = C

Proof of Theorem 3eqtr3r

Step	Hyp	Ref	Expression
1		3eqtr3.3	. 2 ⊢ B = D
2		3eqtr3.1	. . 3 ⊢ A = B
3		3eqtr3.2	. . 3 ⊢ A = C
4	2, 3	eqtr3 1121	. 2 ⊢ B = C
5	1, 4	eqtr3 1121	1 ⊢ D = C

Syntax hints:   = wceq 1091

This theorem is referenced by:  difdifdir 1765  cnvcnv 2661  co01 2664  dfdom2 3288  muladd 4181  isqm1 4525  discrlem1 4713  projlem18 5210  pjclem1 5649  pjc 5654

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-cleq 1097

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