Theorem 19.3vOLD 1988

Description: Obsolete version of 19.3v 1985 as of 20-Oct-2023. (Contributed by Anthony Hart, 13-Sep-2011.) Remove dependency on ax-7 2014. (Revised by Wolf Lammen, 4-Dec-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
19.3vOLD	⊢ (∀𝑥𝜑 ↔ 𝜑)

Distinct variable group:   𝜑,𝑥

Proof of Theorem 19.3vOLD

Step	Hyp	Ref	Expression
1		alex 1825	. 2 ⊢ (∀𝑥𝜑 ↔ ¬ ∃𝑥 ¬ 𝜑)
2		19.9v 1987	. . 3 ⊢ (∃𝑥 ¬ 𝜑 ↔ ¬ 𝜑)
3	2	con2bii 360	. 2 ⊢ (𝜑 ↔ ¬ ∃𝑥 ¬ 𝜑)
4	1, 3	bitr4i 280	1 ⊢ (∀𝑥𝜑 ↔ 𝜑)

Syntax hints:  ¬ wn 3   ↔ wb 208  ∀wal 1534  ∃wex 1779

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969

This theorem depends on definitions:  df-bi 209  df-ex 1780

This theorem is referenced by: (None)