Theorem axie1 2703

Description: The setvar 𝑥 is not free in ∃𝑥𝜑 (intuitionistic logic axiom ax-ie1). (Contributed by Jim Kingdon, 31-Dec-2017.) (New usage is discouraged.)

Assertion

Ref	Expression
axie1	⊢ (∃𝑥𝜑 → ∀𝑥∃𝑥𝜑)

Proof of Theorem axie1

Step	Hyp	Ref	Expression
1		hbe1 2139	1 ⊢ (∃𝑥𝜑 → ∀𝑥∃𝑥𝜑)

Syntax hints:   → wi 4  ∀wal 1537  ∃wex 1782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-10 2137

This theorem depends on definitions:  df-bi 206  df-ex 1783

This theorem is referenced by: (None)