Theorem 3adant3r 1259

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 1232	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1255	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1232	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1002

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 1004

This theorem is referenced by:  addassnqg  7580  mulassnqg  7582  prarloc  7701  ltpopr  7793  ltexprlemfl  7807  ltexprlemfu  7809  addasssrg  7954  axaddass  8070  apmul1  8946  ltmul2  9014  lemul2  9015  dvdscmulr  12347  dvdsmulcr  12348  modremain  12456  ndvdsadd  12458  rpexp12i  12693  xblcntrps  15103  xblcntr  15104