Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Classes
Class equality
eqtr4i
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3eqtri
Metamath Proof Explorer
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Theorem
eqtr4i
Description:
An equality transitivity inference.
(Contributed by
NM
, 26-May-1993)
Ref
Expression
Hypotheses
eqtr4i.1
⊢
A
=
B
eqtr4i.2
⊢
C
=
B
Assertion
eqtr4i
⊢
A
=
C
Proof
Step
Hyp
Ref
Expression
1
eqtr4i.1
⊢
A
=
B
2
eqtr4i.2
⊢
C
=
B
3
2
eqcomi
⊢
B
=
C
4
1
3
eqtri
⊢
A
=
C