Axiom ax-7 676

Description: Axiom of Quantifier Commutation. This axiom says universal quantifiers can be swapped. One of the 4 axioms of pure predicate calculus. Axiom scheme C6' in [Megill] p. 448 (p. 16 of the preprint). Also appears as Lemma 12 of [Monk2] p. 109.

Assertion

Ref	Expression
ax-7	⊢ (∀x∀yφ → ∀y∀xφ)

Detailed syntax breakdown of Axiom ax-7

Step	Hyp	Ref	Expression
1		wph	. . . 4 wff φ
2		vy	. . . 4 set y
3	1, 2	wal 672	. . 3 wff ∀yφ
4		vx	. . 3 set x
5	3, 4	wal 672	. 2 wff ∀x∀yφ
6	1, 4	wal 672	. . 3 wff ∀xφ
7	6, 2	wal 672	. 2 wff ∀y∀xφ
8	5, 7	wi 2	1 wff (∀x∀yφ → ∀y∀xφ)

This axiom is referenced by:  a7s 689  hbal 700  alcom 715  hbald 790  eq5 824  cbv1 845  sbal1 996

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