Theorem nfmod

Description: Bound-variable hypothesis builder for the at-most-one quantifier. Deduction version of nfmo . Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfmodv when possible. (Contributed by Mario Carneiro, 14-Nov-2016) (New usage is discouraged.)

	Ref	Expression
Hypotheses	nfmod.1	⊢ Ⅎ 𝑦 𝜑
	nfmod.2	⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 )
Assertion	nfmod	⊢ ( 𝜑 → Ⅎ 𝑥 ∃* 𝑦 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		nfmod.1	⊢ Ⅎ 𝑦 𝜑
2		nfmod.2	⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 )
3	2	adantr	⊢ ( ( 𝜑 ∧ ¬ ∀ 𝑥 𝑥 = 𝑦 ) → Ⅎ 𝑥 𝜓 )
4	1 3	nfmod2	⊢ ( 𝜑 → Ⅎ 𝑥 ∃* 𝑦 𝜓 )