Theorem qswap-P8.VR 1106

Description: qswap-P8 1105 with variable restriction. †

'𝑥' cannot occur in '𝜑'.

Assertion

Ref	Expression
qswap-P8.VR	⊢ (∃𝑥𝜑 ↔ ∀𝑥𝜑)

Distinct variable group:   𝜑,𝑥

Proof of Theorem qswap-P8.VR

Step	Hyp	Ref	Expression
1		ndnfrv-P7.1 826	. 2 ⊢ Ⅎ𝑥𝜑
2	1	qswap-P8 1105	1 ⊢ (∃𝑥𝜑 ↔ ∀𝑥𝜑)

Syntax hints:  ∀wff-forall 8   ↔ wff-bi 104  ∃wff-exists 595

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-L11 28  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  df-psub-D6.2 716

This theorem is referenced by: (None)