Theorem ndalli-P7.17.RC 883

Description: Inference form of ndalli-P7.17 842. †

Hypotheses

Ref	Expression
ndalli-P7.17.RC.1	⊢ Ⅎ𝑦𝜑
ndalli-P7.17.RC.2	⊢ [𝑦 / 𝑥]𝜑

Assertion

Ref	Expression
ndalli-P7.17.RC	⊢ ∀𝑥𝜑

Distinct variable group:   𝑥,𝑦

Proof of Theorem ndalli-P7.17.RC

Step	Hyp	Ref	Expression
1		ndalli-P7.17.RC.1	. . 3 ⊢ Ⅎ𝑦𝜑
2		ndalli-P7.17.RC.2	. . . 4 ⊢ [𝑦 / 𝑥]𝜑
3	2	rcp-NDIMP0addall 207	. . 3 ⊢ (⊤ → [𝑦 / 𝑥]𝜑)
4	1, 3	ndalli-P7.17.VR1of2 864	. 2 ⊢ (⊤ → ∀𝑥𝜑)
5	4	ndtruee-P3.18 183	1 ⊢ ∀𝑥𝜑

Syntax hints:  term-obj 1  ∀wff-forall 8  ⊤wff-true 153  Ⅎwff-nfree 681  [wff-psub 714

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:  ndalli-P7.17.RC.VR  884