Theorem 2ax17 1640

Description: Quantification of two variables over a formula in which they do not occur. (Contributed by Alan Sare, 12-Apr-2011.)

Assertion

Ref	Expression
2ax17	⊢ (φ → ∀x∀yφ)

Distinct variable groups:   φ,x   φ,y

Proof of Theorem 2ax17

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (φ → φ)
2	1	alrimivv 1632	1 ⊢ (φ → ∀x∀yφ)

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616

This theorem is referenced by: (None)