Theorem trnspeq-P4c 537

Description: Transposition Equivalence Law (trnsp-P3.31c 285 and trnsp-P3.31d 288).

Assertion

Ref	Expression
trnspeq-P4c	⊢ ((𝜑 → 𝜓) ↔ (¬ 𝜓 → ¬ 𝜑))

Proof of Theorem trnspeq-P4c

Step	Hyp	Ref	Expression
1		trnsp-P3.31c.CL 287	. 2 ⊢ ((𝜑 → 𝜓) → (¬ 𝜓 → ¬ 𝜑))
2		trnsp-P3.31d.CL 290	. 2 ⊢ ((¬ 𝜓 → ¬ 𝜑) → (𝜑 → 𝜓))
3	1, 2	rcp-NDBII0 239	1 ⊢ ((𝜑 → 𝜓) ↔ (¬ 𝜓 → ¬ 𝜑))

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ↔ wff-bi 104

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

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161

This theorem is referenced by:  alloverimex-P5  601