Theorem ancr 547

Description: Conjoin antecedent to right of consequent. (Contributed by NM, 15-Aug-1994.)

Assertion

Ref	Expression
ancr	⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∧ 𝜑)))

Proof of Theorem ancr

Step	Hyp	Ref	Expression
1		pm3.21 472	. 2 ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑)))
2	1	a2i 14	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∧ 𝜑)))

Syntax hints:   → wi 4   ∧ wa 396

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  df-an 397

This theorem is referenced by:  bimsc1  841  reupick2  4254  intmin4  4908  bnj1098  32763  lukshef-ax2  34604  bj-opelid  35327  poimirlem25  35802  pm14.122b  42041