Theorem 3adant3r 1181

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 1154	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1177	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1154	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 930

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 932

This theorem is referenced by:  addassnqg  7091  mulassnqg  7093  prarloc  7212  ltpopr  7304  ltexprlemfl  7318  ltexprlemfu  7320  addasssrg  7452  axaddass  7557  apmul1  8409  ltmul2  8472  lemul2  8473  dvdscmulr  11317  dvdsmulcr  11318  modremain  11421  ndvdsadd  11423  rpexp12i  11626  xblcntrps  12341  xblcntr  12342