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  7497  mulassnqg  7499  prarloc  7618  ltpopr  7710  ltexprlemfl  7724  ltexprlemfu  7726  addasssrg  7871  axaddass  7987  apmul1  8863  ltmul2  8931  lemul2  8932  dvdscmulr  12164  dvdsmulcr  12165  modremain  12273  ndvdsadd  12275  rpexp12i  12510  xblcntrps  14918  xblcntr  14919