Theorem mae-P3.23.RC 258

Description: Inference Form of mae-P3.23 257. †

Hypotheses

Ref	Expression
mae-P3.23.RC.1	⊢ (𝜑 → (𝜓 → 𝜒))
mae-P3.23.RC.2	⊢ 𝜓

Assertion

Ref	Expression
mae-P3.23.RC	⊢ (𝜑 → 𝜒)

Proof of Theorem mae-P3.23.RC

Step	Hyp	Ref	Expression
1		mae-P3.23.RC.1	. . . 4 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 → (𝜓 → 𝜒)))
3		mae-P3.23.RC.2	. . . 4 ⊢ 𝜓
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → 𝜓)
5	2, 4	mae-P3.23 257	. 2 ⊢ (⊤ → (𝜑 → 𝜒))
6	5	ndtruee-P3.18 183	1 ⊢ (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

This theorem is referenced by:  lemma-L5.02a  653  exipsub-P6  720  lemma-L6.04a  749  dfpsubv-P7  977  example-E7.1b  1075