Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Unordered and ordered pairs
oteq2d
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oteq3d
Metamath Proof Explorer
Ascii
Unicode
Theorem
oteq2d
Description:
Equality deduction for ordered triples.
(Contributed by
Mario Carneiro
, 11-Jan-2017)
Ref
Expression
Hypothesis
oteq1d.1
⊢
φ
→
A
=
B
Assertion
oteq2d
⊢
φ
→
C
A
D
=
C
B
D
Proof
Step
Hyp
Ref
Expression
1
oteq1d.1
⊢
φ
→
A
=
B
2
oteq2
⊢
A
=
B
→
C
A
D
=
C
B
D
3
1
2
syl
⊢
φ
→
C
A
D
=
C
B
D