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	|- ( ph -> ( ps -> ch ) )

Assertion

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

Proof of Theorem a1dd

Step	Hyp	Ref	Expression
1		a1dd.1	. 2 |- ( ph -> ( ps -> ch ) )
2		ax-1 6	. 2 |- ( ch -> ( th -> ch ) )
3	1, 2	syl6 33	1 |- ( ph -> ( ps -> ( th -> ch ) ) )

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  exmidsssnc  4340  nnsub  9346  difelfzle  10552  facdiv  11192  facwordi  11194  faclbnd  11195  pfxccat3  11522  dvdsabseq  12633  divgcdcoprm0  12898  exprmfct  12936  prmfac1  12950  pockthg  13159  clwwlknonex2lem2  16845  bj-inf2vnlem2  17163