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ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Classes
Class equality
syl5req
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eqtr3id
Metamath Proof Explorer
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Theorem
syl5req
Description:
An equality transitivity deduction.
(Contributed by
NM
, 29-Mar-1998)
Ref
Expression
Hypotheses
syl5req.1
⊢
A
=
B
syl5req.2
⊢
φ
→
B
=
C
Assertion
syl5req
⊢
φ
→
C
=
A
Proof
Step
Hyp
Ref
Expression
1
syl5req.1
⊢
A
=
B
2
syl5req.2
⊢
φ
→
B
=
C
3
1
2
syl5eq
⊢
φ
→
A
=
C
4
3
eqcomd
⊢
φ
→
C
=
A