Theorem nfrall1-P6 741

Description: ENF Over Universal Quantifier (same variable).

See nfrall1w-P6 692 for a version that requires only FOL axioms.

Assertion

Ref	Expression
nfrall1-P6	⊢ Ⅎ𝑥∀𝑥𝜑

Proof of Theorem nfrall1-P6

Step	Hyp	Ref	Expression
1		genall-P6 737	. 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑)
2	1	gennfr-P6 734	1 ⊢ Ⅎ𝑥∀𝑥𝜑

Syntax hints:  ∀wff-forall 8  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-L5 17  ax-L6 18  ax-L7 19  ax-L10 27  ax-L12 29

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:  lemma-L6.05a  764  lemma-L6.06a  766  lemma-L6.07a-L1  770  lemma-L6.07a-L2  771  psuball1-P6  793  nfrnfr-P6  821  ndnfrall1-P7.7  832