Theorem anc2l 538

Description: Conjoin antecedent to left of consequent in nested implication. (Contributed by NM, 10-Aug-1994.) (Proof shortened by Wolf Lammen, 14-Jul-2013.)

Assertion

Ref	Expression
anc2l	⊢ ((φ → (ψ → χ)) → (φ → (ψ → (φ ∧ χ))))

Proof of Theorem anc2l

Step	Hyp	Ref	Expression
1		pm5.42 531	. 2 ⊢ ((φ → (ψ → χ)) ↔ (φ → (ψ → (φ ∧ χ))))
2	1	biimpi 186	1 ⊢ ((φ → (ψ → χ)) → (φ → (ψ → (φ ∧ χ))))

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: (None)