Theorem pm10.53

Description: Theorem *10.53 in WhiteheadRussell p. 155. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	pm10.53	⊢ ( ¬ ∃ 𝑥 𝜑 → ∀ 𝑥 ( 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.21	⊢ ( ¬ ∃ 𝑥 𝜑 → ( ∃ 𝑥 𝜑 → ∀ 𝑥 𝜓 ) )
2		19.38	⊢ ( ( ∃ 𝑥 𝜑 → ∀ 𝑥 𝜓 ) → ∀ 𝑥 ( 𝜑 → 𝜓 ) )
3	1 2	syl	⊢ ( ¬ ∃ 𝑥 𝜑 → ∀ 𝑥 ( 𝜑 → 𝜓 ) )