Theorem anbi2 688

Description: Introduce a left conjunct to both sides of a logical equivalence. (Contributed by NM, 16-Nov-2013.)

Assertion

Ref	Expression
anbi2	⊢ ((φ ↔ ψ) → ((χ ∧ φ) ↔ (χ ∧ ψ)))

Proof of Theorem anbi2

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((φ ↔ ψ) → (φ ↔ ψ))
2	1	anbi2d 684	1 ⊢ ((φ ↔ ψ) → ((χ ∧ φ) ↔ (χ ∧ ψ)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 176   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)