Theorem 19.3vOLD 1696

Description: Obsolete version of 19.3v 1665 as of 4-Dec-2017. (Contributed by NM, 1-Aug-2017.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
19.3vOLD	⊢ (∀xφ ↔ φ)

Distinct variable group:   φ,x

Proof of Theorem 19.3vOLD

Step	Hyp	Ref	Expression
1		spvw 1666	. 2 ⊢ (∀xφ → φ)
2		ax-17 1616	. 2 ⊢ (φ → ∀xφ)
3	1, 2	impbii 180	1 ⊢ (∀xφ ↔ φ)

Syntax hints:   ↔ wb 176  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by: (None)