This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem chvarvv

Description: Implicit substitution of y for x into a theorem. Version of chvarv with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 20-Apr-1994) (Revised by BJ, 31-May-2019)

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

Proof

Step	Hyp	Ref	Expression
1		chvarvv.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
2		chvarvv.2	⊢ 𝜑
3	1	spvv	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )
4	3 2	mpg	⊢ 𝜓