Metamath Proof Explorer

Theorem 19.9

Description: A wff may be existentially quantified with a variable not free in it. Version of 19.3 with an existential quantifier. Theorem 19.9 of Margaris p. 89. See 19.9v for a version requiring fewer axioms. (Contributed by FL, 24-Mar-2007) (Revised by Mario Carneiro, 24-Sep-2016) (Proof shortened by Wolf Lammen, 30-Dec-2017) Revised to shorten other proofs. (Revised by Wolf Lammen, 14-Jul-2020)

Ref Expression
Hypothesis 19.9.1 x φ
Assertion 19.9 x φ φ


Step Hyp Ref Expression
1 19.9.1 x φ
2 19.9t x φ x φ φ
3 1 2 ax-mp x φ φ