Theorem imsubl-P1.7b.AC.SH 56

Description: Deductive Form of imsubl-P1.7b 54.

Hypothesis

Ref	Expression
imsubl-P1.7b.AC.SH.1	⊢ (𝛾 → (𝜑 → 𝜓))

Assertion

Ref	Expression
imsubl-P1.7b.AC.SH	⊢ (𝛾 → ((𝜓 → 𝜒) → (𝜑 → 𝜒)))

Proof of Theorem imsubl-P1.7b.AC.SH

Step	Hyp	Ref	Expression
1		imsubl-P1.7b.AC.SH.1	. 2 ⊢ (𝛾 → (𝜑 → 𝜓))
2		imsubl-P1.7b 54	. . . 4 ⊢ ((𝜑 → 𝜓) → ((𝜓 → 𝜒) → (𝜑 → 𝜒)))
3	2	axL1.SH 30	. . 3 ⊢ (𝛾 → ((𝜑 → 𝜓) → ((𝜓 → 𝜒) → (𝜑 → 𝜒))))
4	3	rcp-FR1.SH 40	. 2 ⊢ ((𝛾 → (𝜑 → 𝜓)) → (𝛾 → ((𝜓 → 𝜒) → (𝜑 → 𝜒))))
5	1, 4	ax-MP 14	1 ⊢ (𝛾 → ((𝜓 → 𝜒) → (𝜑 → 𝜒)))

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:  subiml-P2.8a  128