Theorem ancl 529

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		pm3.2 434	. 2 ⊢ (φ → (ψ → (φ ∧ ψ)))
2	1	a2i 12	1 ⊢ ((φ → ψ) → (φ → (φ ∧ ψ)))

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by:  equs4  1959  eupickbi  2270