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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
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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