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  7356  mulassnqg  7358  prarloc  7477  ltpopr  7569  ltexprlemfl  7583  ltexprlemfu  7585  addasssrg  7730  axaddass  7846  apmul1  8717  ltmul2  8784  lemul2  8785  dvdscmulr  11793  dvdsmulcr  11794  modremain  11899  ndvdsadd  11901  rpexp12i  12120  xblcntrps  13464  xblcntr  13465