Theorem imsubr-P1.7a.SH 52

Description: Inference from imsubr-P1.7a 51.

Hypothesis

Ref	Expression
imsubr-P1.7a.SH.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
imsubr-P1.7a.SH	⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓))

Proof of Theorem imsubr-P1.7a.SH

Step	Hyp	Ref	Expression
1		imsubr-P1.7a.SH.1	. 2 ⊢ (𝜑 → 𝜓)
2		imsubr-P1.7a 51	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))
3	1, 2	ax-MP 14	1 ⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓))

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:  trnsp-P1.15b  78  trnsp-P1.15c  80