Theorem ndalle-P7.18.RC 885

Description: Inference Form of ndalle-P7.18 843. †

Hypothesis

Ref	Expression
ndalle-P7.18.RC.1	⊢ ∀𝑥𝜑

Assertion

Ref	Expression
ndalle-P7.18.RC	⊢ [𝑡 / 𝑥]𝜑

Proof of Theorem ndalle-P7.18.RC

Step	Hyp	Ref	Expression
1		ndalle-P7.18.RC.1	. . . 4 ⊢ ∀𝑥𝜑
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → ∀𝑥𝜑)
3	2	ndalle-P7.18 843	. 2 ⊢ (⊤ → [𝑡 / 𝑥]𝜑)
4	3	ndtruee-P3.18 183	1 ⊢ [𝑡 / 𝑥]𝜑

Syntax hints:  ∀wff-forall 8  ⊤wff-true 153  [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

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-true-D2.4 155  df-psub-D6.2 716

This theorem is referenced by: (None)