Database
CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
Logical conjunction
ad2antll
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ad3antrrr
Metamath Proof Explorer
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Theorem
ad2antll
Description:
Deduction adding conjuncts to antecedent.
(Contributed by
NM
, 19-Oct-1999)
Ref
Expression
Hypothesis
ad2ant.1
⊢
φ
→
ψ
Assertion
ad2antll
⊢
χ
∧
θ
∧
φ
→
ψ
Proof
Step
Hyp
Ref
Expression
1
ad2ant.1
⊢
φ
→
ψ
2
1
adantl
⊢
θ
∧
φ
→
ψ
3
2
adantl
⊢
χ
∧
θ
∧
φ
→
ψ