Theorem bj-nfxfr 31794

Description: Proof of nfxfr 1771 from bj-nfbi 31793. (Contributed by BJ, 6-May-2019.)

Hypotheses

Ref	Expression
bj-nfxfr.1	⊢ (𝜑 ↔ 𝜓)
bj-nfxfr.2	⊢ ℲℲ𝑥𝜑

Assertion

Ref	Expression
bj-nfxfr	⊢ ℲℲ𝑥𝜓

Proof of Theorem bj-nfxfr

Step	Hyp	Ref	Expression
1		bj-nfxfr.2	. 2 ⊢ ℲℲ𝑥𝜑
2		bj-nfbi 31793	. . 3 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (ℲℲ𝑥𝜑 ↔ ℲℲ𝑥𝜓))
3		bj-nfxfr.1	. . 3 ⊢ (𝜑 ↔ 𝜓)
4	2, 3	mpg 1715	. 2 ⊢ (ℲℲ𝑥𝜑 ↔ ℲℲ𝑥𝜓)
5	1, 4	mpbi 219	1 ⊢ ℲℲ𝑥𝜓

Syntax hints:   ↔ wb 195  ℲℲwnff 31764

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728

This theorem depends on definitions:  df-bi 196  df-ex 1696  df-bj-nf 31765

This theorem is referenced by: (None)