Theorem 3adant3r 1262

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Hypothesis

Ref	Expression
3adant1l.1	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
3adant3r	|- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Proof of Theorem 3adant3r

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3com13 1235	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1258	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1235	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1005

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1007

This theorem is referenced by:  addassnqg  7713  mulassnqg  7715  prarloc  7834  ltpopr  7926  ltexprlemfl  7940  ltexprlemfu  7942  addasssrg  8087  axaddass  8203  apmul1  9079  ltmul2  9147  lemul2  9148  dvdscmulr  12531  dvdsmulcr  12532  modremain  12640  ndvdsadd  12642  rpexp12i  12877  xblcntrps  15404  xblcntr  15405