Theorem mpdi 38

Description: A nested modus ponens deduction. (Contributed by NM, 16-Apr-2005.) (Proof shortened by O'Cat, 15-Jan-2008.)

Hypotheses

Ref	Expression
mpdi.1	⊢ (𝜓 → 𝜒)
mpdi.2	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Assertion

Ref	Expression
mpdi	⊢ (𝜑 → (𝜓 → 𝜃))

Proof of Theorem mpdi

Step	Hyp	Ref	Expression
1		mpdi.1	. . 3 ⊢ (𝜓 → 𝜒)
2	1	a1i 9	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
3		mpdi.2	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
4	2, 3	mpdd 36	1 ⊢ (𝜑 → (𝜓 → 𝜃))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7

This theorem is referenced by:  mpii  39  pm2.43d  44  gencbval  2602  suctr  4158  tfrlem9  5935  lbzbi  8551  flqeqceilz  9160  bj-inf2vnlem2  10096