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 ) ) )

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  9182  difelfzle  10369  facdiv  11001  facwordi  11003  faclbnd  11004  pfxccat3  11319  dvdsabseq  12426  divgcdcoprm0  12691  exprmfct  12728  prmfac1  12742  pockthg  12948  clwwlknonex2lem2  16308  bj-inf2vnlem2  16617