Theorem pm5.74d 238

Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 21-Mar-1996.)

Hypothesis

Ref	Expression
pm5.74d.1	⊢ (φ → (ψ → (χ ↔ θ)))

Assertion

Ref	Expression
pm5.74d	⊢ (φ → ((ψ → χ) ↔ (ψ → θ)))

Proof of Theorem pm5.74d

Step	Hyp	Ref	Expression
1		pm5.74d.1	. 2 ⊢ (φ → (ψ → (χ ↔ θ)))
2		pm5.74 235	. 2 ⊢ ((ψ → (χ ↔ θ)) ↔ ((ψ → χ) ↔ (ψ → θ)))
3	1, 2	sylib 188	1 ⊢ (φ → ((ψ → χ) ↔ (ψ → θ)))

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

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

This theorem is used by:  imbi2d  307  imim21b  356  pm5.74da  668  2mos  2283  dfiin2g  4001