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  7569  mulassnqg  7571  prarloc  7690  ltpopr  7782  ltexprlemfl  7796  ltexprlemfu  7798  addasssrg  7943  axaddass  8059  apmul1  8935  ltmul2  9003  lemul2  9004  dvdscmulr  12331  dvdsmulcr  12332  modremain  12440  ndvdsadd  12442  rpexp12i  12677  xblcntrps  15087  xblcntr  15088