Theorem spvwOLD 1695

Description: Obsolete version of spvw 1666 as of 4-Dec-2017. (Contributed by NM, 10-Apr-2017.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
spvwOLD	⊢ (∀xφ → φ)

Distinct variable group:   φ,x

Proof of Theorem spvwOLD

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		biidd 228	. 2 ⊢ (x = y → (φ ↔ φ))
2	1	spw 1694	1 ⊢ (∀xφ → φ)

Syntax hints:   → wi 4  ∀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  ax-8 1675

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

This theorem is referenced by: (None)