Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Classes
Class equality
eqtr3i
Next ⟩
eqtr4i
Metamath Proof Explorer
Ascii
Unicode
Theorem
eqtr3i
Description:
An equality transitivity inference.
(Contributed by
NM
, 6-May-1994)
Ref
Expression
Hypotheses
eqtr3i.1
⊢
A
=
B
eqtr3i.2
⊢
A
=
C
Assertion
eqtr3i
⊢
B
=
C
Proof
Step
Hyp
Ref
Expression
1
eqtr3i.1
⊢
A
=
B
2
eqtr3i.2
⊢
A
=
C
3
1
eqcomi
⊢
B
=
A
4
3
2
eqtri
⊢
B
=
C