Database
CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
Logical conjunction
biimpar
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biimpac
Metamath Proof Explorer
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Theorem
biimpar
Description:
Importation inference from a logical equivalence.
(Contributed by
NM
, 3-May-1994)
Ref
Expression
Hypothesis
biimpa.1
⊢
φ
→
ψ
↔
χ
Assertion
biimpar
⊢
φ
∧
χ
→
ψ
Proof
Step
Hyp
Ref
Expression
1
biimpa.1
⊢
φ
→
ψ
↔
χ
2
1
biimprd
⊢
φ
→
χ
→
ψ
3
2
imp
⊢
φ
∧
χ
→
ψ