Theorem ancl 545

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		pm3.2 470	. 2 ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜓)))
2	1	a2i 14	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜑 ∧ 𝜓)))

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:  exintr  1895  bnj1118  32964  bnj1128  32970  bnj1145  32973  bnj1174  32983