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CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Predicate calculus with equality: Auxiliary axiom schemes (4 schemes)
Axiom scheme ax-12 (Substitution)
sps
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2sp
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Theorem
sps
Description:
Generalization of antecedent.
(Contributed by
NM
, 5-Jan-1993)
Ref
Expression
Hypothesis
sps.1
⊢
φ
→
ψ
Assertion
sps
⊢
∀
x
φ
→
ψ
Proof
Step
Hyp
Ref
Expression
1
sps.1
⊢
φ
→
ψ
2
sp
⊢
∀
x
φ
→
φ
3
2
1
syl
⊢
∀
x
φ
→
ψ