Theorem nfxfrOLD 1837

Description: Obsolete proof of nfxfr 1779 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfbiiOLD.1	⊢ (𝜑 ↔ 𝜓)
nfxfrOLD.2	⊢ Ⅎ𝑥𝜓

Assertion

Ref	Expression
nfxfrOLD	⊢ Ⅎ𝑥𝜑

Proof of Theorem nfxfrOLD

Step	Hyp	Ref	Expression
1		nfxfrOLD.2	. 2 ⊢ Ⅎ𝑥𝜓
2		nfbiiOLD.1	. . 3 ⊢ (𝜑 ↔ 𝜓)
3	2	nfbiiOLD 1836	. 2 ⊢ (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓)
4	1, 3	mpbir 221	1 ⊢ Ⅎ𝑥𝜑

Syntax hints:   ↔ wb 196  ℲwnfOLD 1709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-nfOLD 1721

This theorem is referenced by:  nfnf1OLDOLD  2208  nfnanOLD  2238  nf3anOLD  2239  nforOLD  2244  nf3orOLD  2245