Theorem pm5.13dc 907

Description: An implication holds in at least one direction, where one proposition is decidable. Based on theorem *5.13 of [WhiteheadRussell] p. 123. (Contributed by Jim Kingdon, 30-Mar-2018.)

Assertion

Ref	Expression
pm5.13dc	⊢ (DECID 𝜓 → ((𝜑 → 𝜓) ∨ (𝜓 → 𝜑)))

Proof of Theorem pm5.13dc

Step	Hyp	Ref	Expression
1		pm5.14dc 906	1 ⊢ (DECID 𝜓 → ((𝜑 → 𝜓) ∨ (𝜓 → 𝜑)))

Syntax hints:   → wi 4   ∨ wo 703  DECID wdc 829

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 610  ax-io 704

This theorem depends on definitions:  df-bi 116  df-dc 830

This theorem is referenced by: (None)