Axiom ax-5 1557

Description: Axiom of Quantified Implication. Axiom C4 of [Monk2] p. 105. (Contributed by NM, 5-Aug-1993.)

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 4	. . 3 wff (φ → ψ)
4		vx	. . 3 setvar x
5	3, 4	wal 1540	. 2 wff ∀x(φ → ψ)
6	1, 4	wal 1540	. . 3 wff ∀xφ
7	2, 4	wal 1540	. . 3 wff ∀xψ
8	6, 7	wi 4	. 2 wff (∀xφ → ∀xψ)
9	5, 8	wi 4	1 wff (∀x(φ → ψ) → (∀xφ → ∀xψ))

This axiom is referenced by:  alim  1558  alimi  1559  spfw  1691  spw  1694  ax5o  1749  19.21t  1795  a16g  1945