Theorem ancl 547

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

Assertion

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

Proof of Theorem ancl

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

Syntax hints:   → wi 4   ∧ wa 398

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 209  df-an 399

This theorem is referenced by:  exintr  1887  bnj1118  32249  bnj1128  32255  bnj1145  32258  bnj1174  32268