Theorem pm4.45im 828

Description: Conjunction with implication. Compare Theorem *4.45 of [WhiteheadRussell] p. 119. (Contributed by NM, 17-May-1998.)

Assertion

Ref	Expression
pm4.45im	⊢ (𝜑 ↔ (𝜑 ∧ (𝜓 → 𝜑)))

Proof of Theorem pm4.45im

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (𝜑 → (𝜓 → 𝜑))
2	1	pm4.71i 563	1 ⊢ (𝜑 ↔ (𝜑 ∧ (𝜓 → 𝜑)))

Syntax hints:   → wi 4   ↔ wb 209   ∧ wa 399

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 210  df-an 400

This theorem is referenced by:  difdif  4062