Theorem nfxfrdOLD 1838

Description: Obsolete proof of nfxfrd 1780 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfbiiOLD.1	⊢ (𝜑 ↔ 𝜓)
nfxfrdOLD.2	⊢ (𝜒 → Ⅎ𝑥𝜓)

Assertion

Ref	Expression
nfxfrdOLD	⊢ (𝜒 → Ⅎ𝑥𝜑)

Proof of Theorem nfxfrdOLD

Step	Hyp	Ref	Expression
1		nfxfrdOLD.2	. 2 ⊢ (𝜒 → Ⅎ𝑥𝜓)
2		nfbiiOLD.1	. . 3 ⊢ (𝜑 ↔ 𝜓)
3	2	nfbiiOLD 1836	. 2 ⊢ (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓)
4	1, 3	sylibr 224	1 ⊢ (𝜒 → Ⅎ𝑥𝜑)

Syntax hints:   → wi 4   ↔ 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:  nfandOLD  2232  nf3andOLD  2233  nfbidOLD  2242