Theorem dalloverimex-P7.GENV 1037

Description: dalloverimex-P7 1033 with generalization augmentation (variable restriction). †

'𝑥' cannot occur in '𝛾'.

Hypothesis

Ref	Expression
dalloverimex-P7.GENV.1	⊢ (𝛾 → (𝜑 → (𝜓 → 𝜒)))

Assertion

Ref	Expression
dalloverimex-P7.GENV	⊢ (𝛾 → (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)))

Distinct variable group:   𝛾,𝑥

Proof of Theorem dalloverimex-P7.GENV

Step	Hyp	Ref	Expression
1		dalloverimex-P7.GENV.1	. . 3 ⊢ (𝛾 → (𝜑 → (𝜓 → 𝜒)))
2	1	alli-P7r.VR 991	. 2 ⊢ (𝛾 → ∀𝑥(𝜑 → (𝜓 → 𝜒)))
3	2	dalloverimex-P7 1033	1 ⊢ (𝛾 → (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)))

Syntax hints:  ∀wff-forall 8   → wff-imp 10  ∃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)