Theorem 3adant3r 1237

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 1210	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1233	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1210	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

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 982

This theorem is referenced by:  addassnqg  7444  mulassnqg  7446  prarloc  7565  ltpopr  7657  ltexprlemfl  7671  ltexprlemfu  7673  addasssrg  7818  axaddass  7934  apmul1  8809  ltmul2  8877  lemul2  8878  dvdscmulr  11966  dvdsmulcr  11967  modremain  12073  ndvdsadd  12075  rpexp12i  12296  xblcntrps  14592  xblcntr  14593