Theorem nfceqiOLD 2973

Description: Obsolete proof of nfceqi 2972 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 1804	. . 3 ⊢ Ⅎ𝑥⊤
2		nfcxfr.1	. . . 4 ⊢ 𝐴 = 𝐵
3	2	a1i 11	. . 3 ⊢ (⊤ → 𝐴 = 𝐵)
4	1, 3	nfceqdf 2971	. 2 ⊢ (⊤ → (Ⅎ𝑥𝐴 ↔ Ⅎ𝑥𝐵))
5	4	mptru 1543	1 ⊢ (Ⅎ𝑥𝐴 ↔ Ⅎ𝑥𝐵)

Syntax hints:   ↔ wb 208   = wceq 1536  ⊤wtru 1537  Ⅎwnfc 2960

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-12 2176  ax-ext 2792

This theorem depends on definitions:  df-bi 209  df-an 399  df-tru 1539  df-ex 1780  df-nf 1784  df-cleq 2813  df-clel 2892  df-nfc 2962

This theorem is referenced by: (None)