Theorem 3adant3r 1266

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 1239	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1262	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1239	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  addassnqg  7755  mulassnqg  7757  prarloc  7876  ltpopr  7968  ltexprlemfl  7982  ltexprlemfu  7984  addasssrg  8129  axaddass  8245  apmul1  9126  ltmul2  9194  lemul2  9195  dvdscmulr  12611  dvdsmulcr  12612  modremain  12720  ndvdsadd  12722  rpexp12i  12958  xblcntrps  15656  xblcntr  15657