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ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Classes
Class equality
eqtr2d
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eqtr3d
Metamath Proof Explorer
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Theorem
eqtr2d
Description:
An equality transitivity deduction.
(Contributed by
NM
, 18-Oct-1999)
Ref
Expression
Hypotheses
eqtr2d.1
⊢
φ
→
A
=
B
eqtr2d.2
⊢
φ
→
B
=
C
Assertion
eqtr2d
⊢
φ
→
C
=
A
Proof
Step
Hyp
Ref
Expression
1
eqtr2d.1
⊢
φ
→
A
=
B
2
eqtr2d.2
⊢
φ
→
B
=
C
3
1
2
eqtrd
⊢
φ
→
A
=
C
4
3
eqcomd
⊢
φ
→
C
=
A