Theorem ndnfrex2-P7.10.VR12of2 861

Description: ndnfrex2-P7.10 835 with 2 variable restrictions. †

Neither '𝑥' nor '𝑦' can occur in '𝛾'.

Hypothesis

Ref	Expression
ndnfrex2-P7.10.VR12of2.1	⊢ (𝛾 → Ⅎ𝑥𝜑)

Assertion

Ref	Expression
ndnfrex2-P7.10.VR12of2	⊢ (𝛾 → Ⅎ𝑥∃𝑦𝜑)

Distinct variable group:   𝛾,𝑥,𝑦

Proof of Theorem ndnfrex2-P7.10.VR12of2

Step	Hyp	Ref	Expression
1		ndnfrv-P7.1 826	. 2 ⊢ Ⅎ𝑥𝛾
2		ndnfrv-P7.1 826	. 2 ⊢ Ⅎ𝑦𝛾
3		ndnfrex2-P7.10.VR12of2.1	. 2 ⊢ (𝛾 → Ⅎ𝑥𝜑)
4	1, 2, 3	ndnfrex2-P7.10 835	1 ⊢ (𝛾 → Ⅎ𝑥∃𝑦𝜑)

Syntax hints:   → wff-imp 10  ∃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-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

This theorem is referenced by:  ndnfrex2-P7.10.RC  881