Database
CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
True and false constants
The true constant
tru
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dftru2
Metamath Proof Explorer
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Theorem
tru
Description:
The truth value
T.
is provable.
(Contributed by
Anthony Hart
, 13-Oct-2010)
Ref
Expression
Assertion
tru
⊢
⊤
Proof
Step
Hyp
Ref
Expression
1
id
⊢
∀
x
x
=
x
→
∀
x
x
=
x
2
df-tru
⊢
⊤
↔
∀
x
x
=
x
→
∀
x
x
=
x
3
1
2
mpbir
⊢
⊤