Theorem nfbiOLD 2231

Description: Obsolete proof of nfbi 1821 as of 6-Oct-2021. (Contributed by NM, 26-May-1993.) (Revised by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 2-Jan-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
nfOLD.1	⊢ Ⅎ𝑥𝜑
nfOLD.2	⊢ Ⅎ𝑥𝜓

Assertion

Ref	Expression
nfbiOLD	⊢ Ⅎ𝑥(𝜑 ↔ 𝜓)

Proof of Theorem nfbiOLD

Step	Hyp	Ref	Expression
1		nfOLD.1	. . . 4 ⊢ Ⅎ𝑥𝜑
2	1	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
3		nfOLD.2	. . . 4 ⊢ Ⅎ𝑥𝜓
4	3	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜓)
5	2, 4	nfbidOLD 2230	. 2 ⊢ (⊤ → Ⅎ𝑥(𝜑 ↔ 𝜓))
6	5	trud 1484	1 ⊢ Ⅎ𝑥(𝜑 ↔ 𝜓)

Syntax hints:   ↔ wb 195  ⊤wtru 1476  ℲwnfOLD 1700

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-nfOLD 1712

This theorem is referenced by: (None)