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Theorem a1dd 47
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  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
a1dd  |-  ( ph  ->  ( ps  ->  ( th  ->  ch ) ) )

Proof of Theorem a1dd
StepHypRef Expression
1 a1dd.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 ax-1 5 . 2  |-  ( ch 
->  ( th  ->  ch ) )
31, 2syl6 33 1  |-  ( ph  ->  ( ps  ->  ( th  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  nnsub  8451  difelfzle  9533  facdiv  10134  facwordi  10136  faclbnd  10137  dvdsabseq  11113  divgcdcoprm0  11348  exprmfct  11384  prmfac1  11396  bj-inf2vnlem2  11749
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