Theorem 3adant3r 1235

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 1208	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1231	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1208	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 978

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 980

This theorem is referenced by:  addassnqg  7381  mulassnqg  7383  prarloc  7502  ltpopr  7594  ltexprlemfl  7608  ltexprlemfu  7610  addasssrg  7755  axaddass  7871  apmul1  8745  ltmul2  8813  lemul2  8814  dvdscmulr  11827  dvdsmulcr  11828  modremain  11934  ndvdsadd  11936  rpexp12i  12155  xblcntrps  13916  xblcntr  13917