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Axiom ax-ie1 1382
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 → ∀𝑥𝑥𝜑)

Detailed syntax breakdown of Axiom ax-ie1
StepHypRef Expression
1 wph . . 3 wff 𝜑
2 vx . . 3 setvar 𝑥
31, 2wex 1381 . 2 wff 𝑥𝜑
43, 2wal 1241 . 2 wff 𝑥𝑥𝜑
53, 4wi 4 1 wff (∃𝑥𝜑 → ∀𝑥𝑥𝜑)
Colors of variables: wff set class
This axiom is referenced by:  hbe1  1384  sbidm  1731
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