Theorem alli-P7r 990

Description: Simplified '∀' Introduction Law. †

For the original form, using explicit substitution, see ndalli-P7.17 842. The inference form is axGEN-P7 933.

This is the restatement of a previously proven result. Do not use in proofs. Use alli-P7 947 instead.

Hypotheses

Ref	Expression
alli-P7r.1	⊢ Ⅎ𝑥𝛾
alli-P7r.2	⊢ (𝛾 → 𝜑)

Assertion

Ref	Expression
alli-P7r	⊢ (𝛾 → ∀𝑥𝜑)

Proof of Theorem alli-P7r

Step	Hyp	Ref	Expression
1		alli-P7r.1	. 2 ⊢ Ⅎ𝑥𝛾
2		alli-P7r.2	. 2 ⊢ (𝛾 → 𝜑)
3	1, 2	alli-P7 947	1 ⊢ (𝛾 → ∀𝑥𝜑)

Syntax hints:  ∀wff-forall 8   → wff-imp 10  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  df-psub-D6.2 716

This theorem is referenced by: (None)