Theorem chvarv

Description: Implicit substitution of y for x into a theorem. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker chvarvv if possible. (Contributed by NM, 20-Apr-1994) (Proof shortened by Wolf Lammen, 22-Apr-2018) (New usage is discouraged.)

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

Proof

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