Database
CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Predicate calculus with equality: Tarski's system S2 (1 rule, 6 schemes)
Axiom scheme ax-7 (Equality)
ax6evr
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ax7
Metamath Proof Explorer
Ascii
Structured
Theorem
ax6evr
Description:
A commuted form of
ax6ev
.
(Contributed by
BJ
, 7-Dec-2020)
Ref
Expression
Assertion
ax6evr
⊢
∃
𝑥
𝑦
=
𝑥
Proof
Step
Hyp
Ref
Expression
1
ax6ev
⊢
∃
𝑥
𝑥
=
𝑦
2
equcomiv
⊢
(
𝑥
=
𝑦
→
𝑦
=
𝑥
)
3
1
2
eximii
⊢
∃
𝑥
𝑦
=
𝑥