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CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
Abbreviated conjunction and disjunction of three wff's
3adant2
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3adant3
Metamath Proof Explorer
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Theorem
3adant2
Description:
Deduction adding a conjunct to antecedent.
(Contributed by
NM
, 16-Jul-1995)
Ref
Expression
Hypothesis
3adant.1
⊢
φ
∧
ψ
→
χ
Assertion
3adant2
⊢
φ
∧
θ
∧
ψ
→
χ
Proof
Step
Hyp
Ref
Expression
1
3adant.1
⊢
φ
∧
ψ
→
χ
2
1
adantlr
⊢
φ
∧
θ
∧
ψ
→
χ
3
2
3impa
⊢
φ
∧
θ
∧
ψ
→
χ