Theorem imsubl-P1.7b.SH 55

Description: Inference from imsubl-P1.7b 54.

Hypothesis

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

Assertion

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

Proof of Theorem imsubl-P1.7b.SH

Step	Hyp	Ref	Expression
1		imsubl-P1.7b.SH.1	. 2 ⊢ (𝜑 → 𝜓)
2		imsubl-P1.7b 54	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜓 → 𝜒) → (𝜑 → 𝜒)))
3	1, 2	ax-MP 14	1 ⊢ ((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:  nclav-P1.14  73  trnsp-P1.15a  76