Theorem axL2.SH 31

Description: Inference from ax-L2 12.

Hypothesis

Ref	Expression
axL2.SH.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
axL2.SH	⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒))

Proof of Theorem axL2.SH

Step	Hyp	Ref	Expression
1		axL2.SH.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		ax-L2 12	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒)))
3	1, 2	ax-MP 14	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒))

Syntax hints:   → wff-imp 10

This theorem was proved from axioms:  ax-L2 12  ax-MP 14

This theorem is referenced by:  mae-P1.1  33  syl-P1.2  34  id-P1.4  36  rcp-FR2  41  rcp-FR3  43  clav-P1.12  68  import-L2.1a  91  orelim-P2.11c.AC.3SH  151