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  7697  mulassnqg  7699  prarloc  7818  ltpopr  7910  ltexprlemfl  7924  ltexprlemfu  7926  addasssrg  8071  axaddass  8187  apmul1  9062  ltmul2  9130  lemul2  9131  dvdscmulr  12506  dvdsmulcr  12507  modremain  12615  ndvdsadd  12617  rpexp12i  12852  xblcntrps  15278  xblcntr  15279