Database
CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
True and false constants
The false constant
falimd
Next ⟩
dfnot
Metamath Proof Explorer
Ascii
Structured
Theorem
falimd
Description:
The truth value
F.
implies anything.
(Contributed by
Mario Carneiro
, 9-Feb-2017)
Ref
Expression
Assertion
falimd
⊢
( (
𝜑
∧ ⊥ ) →
𝜓
)
Proof
Step
Hyp
Ref
Expression
1
falim
⊢
( ⊥ →
𝜓
)
2
1
adantl
⊢
( (
𝜑
∧ ⊥ ) →
𝜓
)