Theorem a1dd 48

Description: Deduction introducing a nested embedded antecedent. (Contributed by NM, 17-Dec-2004.) (Proof shortened by O'Cat, 15-Jan-2008.)

Hypothesis

Ref	Expression
a1dd.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
a1dd	⊢ (𝜑 → (𝜓 → (𝜃 → 𝜒)))

Proof of Theorem a1dd

Step	Hyp	Ref	Expression
1		a1dd.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		ax-1 6	. 2 ⊢ (𝜒 → (𝜃 → 𝜒))
3	1, 2	syl6 33	1 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜒)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  exmidsssnc  4293  nnsub  9181  difelfzle  10368  facdiv  10999  facwordi  11001  faclbnd  11002  pfxccat3  11314  dvdsabseq  12407  divgcdcoprm0  12672  exprmfct  12709  prmfac1  12723  pockthg  12929  clwwlknonex2lem2  16288  bj-inf2vnlem2  16566