Theorem chvarvOLD 2252

Description: Obsolete proof of chvarv 2251 as of 14-Jul-2021. (Contributed by NM, 20-Apr-1994.) (Proof shortened by Wolf Lammen, 22-Apr-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
chvarv.1	⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓))
chvarv.2	⊢ 𝜑

Assertion

Ref	Expression
chvarvOLD	⊢ 𝜓

Distinct variable group:   𝜓,𝑥

Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑦)

Proof of Theorem chvarvOLD

Step	Hyp	Ref	Expression
1		nfv 1830	. 2 ⊢ Ⅎ𝑥𝜓
2		chvarv.1	. 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓))
3		chvarv.2	. 2 ⊢ 𝜑
4	1, 2, 3	chvar 2250	1 ⊢ 𝜓

Syntax hints:   → wi 4   ↔ wb 195

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-13 2234

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-nf 1701

This theorem is referenced by: (None)