Theorem ndexi-P7.19.CL 910

Description: Closed Form of ndexi-P7.19 844. †

Assertion

Ref	Expression
ndexi-P7.19.CL	⊢ ([𝑡 / 𝑥]𝜑 → ∃𝑥𝜑)

Proof of Theorem ndexi-P7.19.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. 2 ⊢ ([𝑡 / 𝑥]𝜑 → [𝑡 / 𝑥]𝜑)
2	1	ndexi-P7.19 844	1 ⊢ ([𝑡 / 𝑥]𝜑 → ∃𝑥𝜑)

Syntax hints:   → wff-imp 10  ∃wff-exists 595  [wff-psub 714

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-GEN 15  ax-L4 16  ax-L5 17  ax-L6 18

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161  df-exists-D5.1 596  df-psub-D6.2 716

This theorem is referenced by:  axL4ex-P7  946  cbvex-P7-L1  1065