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CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
Logical conjunction
ancli
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Theorem
ancli
Description:
Deduction conjoining antecedent to left of consequent.
(Contributed by
NM
, 12-Aug-1993)
Ref
Expression
Hypothesis
ancli.1
⊢
φ
→
ψ
Assertion
ancli
⊢
φ
→
φ
∧
ψ
Proof
Step
Hyp
Ref
Expression
1
ancli.1
⊢
φ
→
ψ
2
id
⊢
φ
→
φ
3
2
1
jca
⊢
φ
→
φ
∧
ψ