Theorem wl-equsalcom

Description: This simple equivalence eases substitution of one expression for the other. (Contributed by Wolf Lammen, 1-Sep-2018)

	Ref	Expression
Assertion	wl-equsalcom	⊢ ( ∀ 𝑥 ( 𝑥 = 𝑦 → 𝜑 ) ↔ ∀ 𝑥 ( 𝑦 = 𝑥 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		equcom	⊢ ( 𝑥 = 𝑦 ↔ 𝑦 = 𝑥 )
2	1	imbi1i	⊢ ( ( 𝑥 = 𝑦 → 𝜑 ) ↔ ( 𝑦 = 𝑥 → 𝜑 ) )
3	2	albii	⊢ ( ∀ 𝑥 ( 𝑥 = 𝑦 → 𝜑 ) ↔ ∀ 𝑥 ( 𝑦 = 𝑥 → 𝜑 ) )