Theorem 3adant3r 1238

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 1211	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1234	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1211	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 981

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 983

This theorem is referenced by:  addassnqg  7495  mulassnqg  7497  prarloc  7616  ltpopr  7708  ltexprlemfl  7722  ltexprlemfu  7724  addasssrg  7869  axaddass  7985  apmul1  8861  ltmul2  8929  lemul2  8930  dvdscmulr  12131  dvdsmulcr  12132  modremain  12240  ndvdsadd  12242  rpexp12i  12477  xblcntrps  14885  xblcntr  14886