Theorem nfrex1-P6 742

Description: ENF Over Existential Quantifier (same variable).

See nfrex1w-P6 693 for a version that requires only FOL axioms.

Assertion

Ref	Expression
nfrex1-P6	⊢ Ⅎ𝑥∃𝑥𝜑

Proof of Theorem nfrex1-P6

Step	Hyp	Ref	Expression
1		genex-P6 731	. 2 ⊢ (∃𝑥𝜑 → ∀𝑥∃𝑥𝜑)
2	1	gennfr-P6 734	1 ⊢ Ⅎ𝑥∃𝑥𝜑

Syntax hints:  ∃wff-exists 595  Ⅎwff-nfree 681

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-L10 27

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-nfree-D6.1 682

This theorem is referenced by:  spliteq-P6  776  splitelof-P6  778  psubex1-P6  794  nfrnfr-P6  821  ndnfrex1-P7.8  833