Database
CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Predicate calculus with equality: Tarski's system S2 (1 rule, 6 schemes)
Axiom scheme ax-7 (Equality)
equtr
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equtrr
Metamath Proof Explorer
Ascii
Structured
Theorem
equtr
Description:
A transitive law for equality.
(Contributed by
NM
, 23-Aug-1993)
Ref
Expression
Assertion
equtr
⊢
(
𝑥
=
𝑦
→ (
𝑦
=
𝑧
→
𝑥
=
𝑧
) )
Proof
Step
Hyp
Ref
Expression
1
ax7
⊢
(
𝑦
=
𝑥
→ (
𝑦
=
𝑧
→
𝑥
=
𝑧
) )
2
1
equcoms
⊢
(
𝑥
=
𝑦
→ (
𝑦
=
𝑧
→
𝑥
=
𝑧
) )