Theorem trnsp-P1.15c 80

Description: Transposition Variant C.

Assertion

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

Proof of Theorem trnsp-P1.15c

Step	Hyp	Ref	Expression
1		dneg-P1.13b 72	. . 3 ⊢ (𝜓 → ¬ ¬ 𝜓)
2	1	imsubr-P1.7a.SH 52	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → ¬ ¬ 𝜓))
3		trnsp-P1.15a 76	. 2 ⊢ ((𝜑 → ¬ ¬ 𝜓) → (¬ 𝜓 → ¬ 𝜑))
4	2, 3	syl-P1.2 34	1 ⊢ ((𝜑 → 𝜓) → (¬ 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:  trnsp-P1.15c.SH  81  trnsp-P1.15c.AC.SH  82  import-L2.1a  91