Theorem axL1.AC.SH 45

Description: Deductive Form of ax-L1 11.

Hypothesis

Ref	Expression
axL1.AC.SH.1	⊢ (𝛾 → 𝜑)

Assertion

Ref	Expression
axL1.AC.SH	⊢ (𝛾 → (𝜓 → 𝜑))

Proof of Theorem axL1.AC.SH

Step	Hyp	Ref	Expression
1		axL1.AC.SH.1	. 2 ⊢ (𝛾 → 𝜑)
2		ax-L1 11	. . . 4 ⊢ (𝜑 → (𝜓 → 𝜑))
3	2	axL1.SH 30	. . 3 ⊢ (𝛾 → (𝜑 → (𝜓 → 𝜑)))
4	3	rcp-FR1.SH 40	. 2 ⊢ ((𝛾 → 𝜑) → (𝛾 → (𝜓 → 𝜑)))
5	1, 4	ax-MP 14	1 ⊢ (𝛾 → (𝜓 → 𝜑))

Syntax hints:   → wff-imp 10

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

This theorem is referenced by:  imcomm-P1.6  48  export-P2.10b  142  ndimp-P3.2  167