Theorem pm5.4 393

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		pm5.5 364	. 2 ⊢ (𝜑 → ((𝜑 → 𝜓) ↔ 𝜓))
2	1	pm5.74i 274	1 ⊢ ((𝜑 → (𝜑 → 𝜓)) ↔ (𝜑 → 𝜓))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210

This theorem is used by:  imbibiOLD  397  bj-alnnf  37403  mnuunid  45028