Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Classes
Class equality
syl5eqr
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syl5reqr
Metamath Proof Explorer
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Unicode
Theorem
syl5eqr
Description:
An equality transitivity deduction.
(Contributed by
NM
, 5-Aug-1993)
Ref
Expression
Hypotheses
syl5eqr.1
⊢
B
=
A
syl5eqr.2
⊢
φ
→
B
=
C
Assertion
syl5eqr
⊢
φ
→
A
=
C
Proof
Step
Hyp
Ref
Expression
1
syl5eqr.1
⊢
B
=
A
2
syl5eqr.2
⊢
φ
→
B
=
C
3
1
eqcomi
⊢
A
=
B
4
3
2
syl5eq
⊢
φ
→
A
=
C