Theorem syl5d 73

Description: A nested syllogism deduction. Deduction associated with syl5 34. (Contributed by NM, 14-May-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by Mel L. O'Cat, 2-Feb-2006.)

Hypotheses

Ref	Expression
syl5d.1	⊢ (𝜑 → (𝜓 → 𝜒))
syl5d.2	⊢ (𝜑 → (𝜃 → (𝜒 → 𝜏)))

Assertion

Ref	Expression
syl5d	⊢ (𝜑 → (𝜃 → (𝜓 → 𝜏)))

Proof of Theorem syl5d

Step	Hyp	Ref	Expression
1		syl5d.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	a1d 25	. 2 ⊢ (𝜑 → (𝜃 → (𝜓 → 𝜒)))
3		syl5d.2	. 2 ⊢ (𝜑 → (𝜃 → (𝜒 → 𝜏)))
4	2, 3	syldd 72	1 ⊢ (𝜑 → (𝜃 → (𝜓 → 𝜏)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  syl7  74  syl9  77  imim12d  81  mopick  2622  isofrlem  7280  kmlem9  10057  squeeze0  12032  lcmfunsnlem1  16550  rnglidlmcl  21155  fgss2  23790  ordcmp  36512  linepsubN  39871  pmapsub  39887  relpfrlem  45070  ichreuopeq  47597  bgoldbnnsum3prm  47928  uhgrimedgi  48014  grimedg  48059