Theorem cmb-L2.3.2SH 100

Description: Inference from cmb-L2.3 99.

Hypotheses

Ref	Expression
cmb-L2.3.2SH.1	⊢ 𝜑
cmb-L2.3.2SH.2	⊢ 𝜓

Assertion

Ref	Expression
cmb-L2.3.2SH	⊢ ¬ (𝜑 → ¬ 𝜓)

Proof of Theorem cmb-L2.3.2SH

Step	Hyp	Ref	Expression
1		cmb-L2.3.2SH.2	. 2 ⊢ 𝜓
2		cmb-L2.3.2SH.1	. . 3 ⊢ 𝜑
3		cmb-L2.3 99	. . 3 ⊢ (𝜑 → (𝜓 → ¬ (𝜑 → ¬ 𝜓)))
4	2, 3	ax-MP 14	. 2 ⊢ (𝜓 → ¬ (𝜑 → ¬ 𝜓))
5	1, 4	ax-MP 14	1 ⊢ ¬ (𝜑 → ¬ 𝜓)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10

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

This theorem is referenced by:  mbicmb-P2.1c  103  bijust-P2.2-L1  105