Theorem 19.17

Description: Theorem 19.17 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypothesis	19.17.1	⊢ Ⅎ 𝑥 𝜓
Assertion	19.17	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( ∀ 𝑥 𝜑 ↔ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		19.17.1	⊢ Ⅎ 𝑥 𝜓
2		albi	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜓 ) )
3	1	19.3	⊢ ( ∀ 𝑥 𝜓 ↔ 𝜓 )
4	2 3	bitrdi	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( ∀ 𝑥 𝜑 ↔ 𝜓 ) )