ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  a1dd GIF version

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 → (𝜓𝜒))
Assertion
Ref Expression
a1dd (𝜑 → (𝜓 → (𝜃𝜒)))

Proof of Theorem a1dd
StepHypRef Expression
1 a1dd.1 . 2 (𝜑 → (𝜓𝜒))
2 ax-1 6 . 2 (𝜒 → (𝜃𝜒))
31, 2syl6 33 1 (𝜑 → (𝜓 → (𝜃𝜒)))
Colors of variables: wff set class
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  4204  nnsub  8958  difelfzle  10134  facdiv  10718  facwordi  10720  faclbnd  10721  dvdsabseq  11853  divgcdcoprm0  12101  exprmfct  12138  prmfac1  12152  pockthg  12355  bj-inf2vnlem2  14726
  Copyright terms: Public domain W3C validator