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CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Predicate calculus with equality: Tarski's system S2 (1 rule, 6 schemes)
Axiom scheme ax-4 (Quantified Implication)
eximii
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exa1
Metamath Proof Explorer
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Theorem
eximii
Description:
Inference associated with
eximi
.
(Contributed by
BJ
, 3-Feb-2018)
Ref
Expression
Hypotheses
eximii.1
⊢
∃
x
φ
eximii.2
⊢
φ
→
ψ
Assertion
eximii
⊢
∃
x
ψ
Proof
Step
Hyp
Ref
Expression
1
eximii.1
⊢
∃
x
φ
2
eximii.2
⊢
φ
→
ψ
3
2
eximi
⊢
∃
x
φ
→
∃
x
ψ
4
1
3
ax-mp
⊢
∃
x
ψ