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SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
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First-order logic
Equality and substitution
bj-ssbid2
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bj-ssbid2ALT
Metamath Proof Explorer
Ascii
Structured
Theorem
bj-ssbid2
Description:
A special case of
sbequ2
.
(Contributed by
BJ
, 22-Dec-2020)
Ref
Expression
Assertion
bj-ssbid2
⊢
( [
𝑥
/
𝑥
]
𝜑
→
𝜑
)
Proof
Step
Hyp
Ref
Expression
1
equid
⊢
𝑥
=
𝑥
2
sbequ2
⊢
(
𝑥
=
𝑥
→ ( [
𝑥
/
𝑥
]
𝜑
→
𝜑
) )
3
1
2
ax-mp
⊢
( [
𝑥
/
𝑥
]
𝜑
→
𝜑
)