Theorem imsubr-P3.28b.RC 270

Description: Inference Form of imsubr-P3.28b 269. †

Hypothesis

Ref	Expression
imsubr-P3.28b.RC.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
imsubr-P3.28b.RC	⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓))

Proof of Theorem imsubr-P3.28b.RC

Step	Hyp	Ref	Expression
1		imsubr-P3.28b.RC.1	. . . 4 ⊢ (𝜑 → 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 → 𝜓))
3	2	imsubr-P3.28b 269	. 2 ⊢ (⊤ → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))
4	3	ndtruee-P3.18 183	1 ⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓))

Syntax hints:   → wff-imp 10  ⊤wff-true 153

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

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

This theorem is referenced by:  psubim-P6-L1  789  ndnfrneg-P7.2  827