Theorem imcomm-P3.27.RC 266

Description: Inference Form of imcomm-P3.27 265. †

Hypothesis

Ref	Expression
imcomm-P3.27.RC.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
imcomm-P3.27.RC	⊢ (𝜓 → (𝜑 → 𝜒))

Proof of Theorem imcomm-P3.27.RC

Step	Hyp	Ref	Expression
1		imcomm-P3.27.RC.1	. . . 4 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 → (𝜓 → 𝜒)))
3	2	imcomm-P3.27 265	. 2 ⊢ (⊤ → (𝜓 → (𝜑 → 𝜒)))
4	3	ndtruee-P3.18 183	1 ⊢ (𝜓 → (𝜑 → 𝜒))

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  df-rcp-AND3 161

This theorem is referenced by:  qimeqex-P5-L2  611  lemma-L5.02a  653  lemma-L6.01a  724  lemma-L6.04a  749  dfpsubv-P7  977