Axiom ax-ie1 1493

Description: 𝑥 is bound in ∃𝑥𝜑. One of the axioms of predicate logic. (Contributed by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
ax-ie1	⊢ (∃𝑥𝜑 → ∀𝑥∃𝑥𝜑)

Detailed syntax breakdown of Axiom ax-ie1

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2		vx	. . 3 setvar 𝑥
3	1, 2	wex 1492	. 2 wff ∃𝑥𝜑
4	3, 2	wal 1351	. 2 wff ∀𝑥∃𝑥𝜑
5	3, 4	wi 4	1 wff (∃𝑥𝜑 → ∀𝑥∃𝑥𝜑)

This axiom is referenced by:  hbe1  1495  sbidm  1851