Axiom ax-5 957

Description: Axiom of Quantified Implication. Axiom C4 of [Monk2] p. 105.

Assertion

Ref	Expression
ax-5	⊢ (∀x(φ → ψ) → (∀xφ → ∀xψ))

Detailed syntax breakdown of Axiom ax-5

Step	Hyp	Ref	Expression
1		wph	. . . 4 wff φ
2		wps	. . . 4 wff ψ
3	1, 2	wi 3	. . 3 wff (φ → ψ)
4		vx	. . 3 set x
5	3, 4	wal 951	. 2 wff ∀x(φ → ψ)
6	1, 4	wal 951	. . 3 wff ∀xφ
7	2, 4	wal 951	. . 3 wff ∀xψ
8	6, 7	wi 3	. 2 wff (∀xφ → ∀xψ)
9	5, 8	wi 3	1 wff (∀x(φ → ψ) → (∀xφ → ∀xψ))

This axiom is referenced by:  ax4 969  ax5o 971

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