Theorem nfceqiOLD 2946

Description: Obsolete proof of nfceqi 2945 as of 19-Jun-2023. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 16-Nov-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nfcxfr.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
nfceqiOLD	⊢ (Ⅎ𝑥𝐴 ↔ Ⅎ𝑥𝐵)

Proof of Theorem nfceqiOLD

Step	Hyp	Ref	Expression
1		nftru 1786	. . 3 ⊢ Ⅎ𝑥⊤
2		nfcxfr.1	. . . 4 ⊢ 𝐴 = 𝐵
3	2	a1i 11	. . 3 ⊢ (⊤ → 𝐴 = 𝐵)
4	1, 3	nfceqdf 2944	. 2 ⊢ (⊤ → (Ⅎ𝑥𝐴 ↔ Ⅎ𝑥𝐵))
5	4	mptru 1529	1 ⊢ (Ⅎ𝑥𝐴 ↔ Ⅎ𝑥𝐵)

Syntax hints:   ↔ wb 207   = wceq 1522  ⊤wtru 1523  Ⅎwnfc 2933

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-8 2083  ax-9 2091  ax-12 2141  ax-ext 2769

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1525  df-ex 1762  df-nf 1766  df-cleq 2788  df-clel 2863  df-nfc 2935

This theorem is referenced by: (None)