Theorem 19.3vOLD

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

	Ref	Expression
Assertion	19.3vOLD	⊢ ( ∀ 𝑥 𝜑 ↔ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		alex	⊢ ( ∀ 𝑥 𝜑 ↔ ¬ ∃ 𝑥 ¬ 𝜑 )
2		19.9v	⊢ ( ∃ 𝑥 ¬ 𝜑 ↔ ¬ 𝜑 )
3	2	con2bii	⊢ ( 𝜑 ↔ ¬ ∃ 𝑥 ¬ 𝜑 )
4	1 3	bitr4i	⊢ ( ∀ 𝑥 𝜑 ↔ 𝜑 )