Theorem ancr 556

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		pm3.21 477	. 2 ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑)))
2	1	a2i 15	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∧ 𝜑)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

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  df-an 402

This theorem is used by:  bimsc1  858  reupick2  4284  intmin4  4944  replem  5251  bnj1098  35239  lukshef-ax2  36985  bj-opelid  37859  poimirlem25  38355  pm14.122b  45193