Theorem wl-nax6nfr 33843

Description: All expressions are free of the variable used in the antecedent. (Contributed by Wolf Lammen, 12-Mar-2023.)

Assertion

Ref	Expression
wl-nax6nfr	⊢ (¬ ∃𝑥⊤ → Ⅎ𝑥𝜑)

Proof of Theorem wl-nax6nfr

Step	Hyp	Ref	Expression
1		wl-nax6al 33842	. 2 ⊢ (¬ ∃𝑥⊤ → ∀𝑥𝜑)
2		nftht 1891	. 2 ⊢ (∀𝑥𝜑 → Ⅎ𝑥𝜑)
3	1, 2	syl 17	1 ⊢ (¬ ∃𝑥⊤ → Ⅎ𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1654  ⊤wtru 1657  ∃wex 1878  Ⅎwnf 1882

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908

This theorem depends on definitions:  df-bi 199  df-tru 1660  df-ex 1879  df-nf 1883

This theorem is referenced by: (None)