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ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Classes
Class equality
eqtrdi
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eqtr2di
Metamath Proof Explorer
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Theorem
eqtrdi
Description:
An equality transitivity deduction.
(Contributed by
NM
, 21-Jun-1993)
Ref
Expression
Hypotheses
eqtrdi.1
⊢
φ
→
A
=
B
eqtrdi.2
⊢
B
=
C
Assertion
eqtrdi
⊢
φ
→
A
=
C
Proof
Step
Hyp
Ref
Expression
1
eqtrdi.1
⊢
φ
→
A
=
B
2
eqtrdi.2
⊢
B
=
C
3
2
a1i
⊢
φ
→
B
=
C
4
1
3
eqtrd
⊢
φ
→
A
=
C