Theorem pm5.4 389

Description: Antecedent absorption implication. Theorem *5.4 of [WhiteheadRussell] p. 125. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
pm5.4	⊢ ((𝜑 → (𝜑 → 𝜓)) ↔ (𝜑 → 𝜓))

Proof of Theorem pm5.4

Step	Hyp	Ref	Expression
1		pm5.5 361	. 2 ⊢ (𝜑 → ((𝜑 → 𝜓) ↔ 𝜓))
2	1	pm5.74i 270	1 ⊢ ((𝜑 → (𝜑 → 𝜓)) ↔ (𝜑 → 𝜓))

Syntax hints:   → wi 4   ↔ wb 205

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206

This theorem is referenced by:  mnuunid  41784