Database
CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Predicate calculus with equality: Auxiliary axiom schemes (4 schemes)
Axiom scheme ax-12 (Substitution)
axc4i
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nfal
Metamath Proof Explorer
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Theorem
axc4i
Description:
Inference version of
axc4
.
(Contributed by
NM
, 3-Jan-1993)
Ref
Expression
Hypothesis
axc4i.1
⊢
∀
x
φ
→
ψ
Assertion
axc4i
⊢
∀
x
φ
→
∀
x
ψ
Proof
Step
Hyp
Ref
Expression
1
axc4i.1
⊢
∀
x
φ
→
ψ
2
nfa1
⊢
Ⅎ
x
∀
x
φ
3
2
1
alrimi
⊢
∀
x
φ
→
∀
x
ψ