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ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Classes
Class equality
eqtri
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eqtr2i
Metamath Proof Explorer
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Theorem
eqtri
Description:
An equality transitivity inference.
(Contributed by
NM
, 26-May-1993)
Ref
Expression
Hypotheses
eqtri.1
⊢
A
=
B
eqtri.2
⊢
B
=
C
Assertion
eqtri
⊢
A
=
C
Proof
Step
Hyp
Ref
Expression
1
eqtri.1
⊢
A
=
B
2
eqtri.2
⊢
B
=
C
3
2
eqeq2i
⊢
A
=
B
↔
A
=
C
4
1
3
mpbi
⊢
A
=
C