Theorem trnsp-P1.15c.SH 81

Description: Inference from trnsp-P1.15c 80.

Hypothesis

Ref	Expression
trnsp-P1.15c.SH.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
trnsp-P1.15c.SH	⊢ (¬ 𝜓 → ¬ 𝜑)

Proof of Theorem trnsp-P1.15c.SH

Step	Hyp	Ref	Expression
1		trnsp-P1.15c.SH.1	. 2 ⊢ (𝜑 → 𝜓)
2		trnsp-P1.15c 80	. 2 ⊢ ((𝜑 → 𝜓) → (¬ 𝜓 → ¬ 𝜑))
3	1, 2	ax-MP 14	1 ⊢ (¬ 𝜓 → ¬ 𝜑)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem is referenced by:  ndfalsee-P3.20  185