Theorem 3adant3r 1166

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 1143	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1162	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1143	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 102   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  addassnqg  6572  mulassnqg  6574  prarloc  6693  ltpopr  6785  ltexprlemfl  6799  ltexprlemfu  6801  addasssrg  6933  axaddass  7038  apmul1  7876  ltmul2  7934  lemul2  7935  dvdscmulr  10224  dvdsmulcr  10225  modremain  10329  ndvdsadd  10331  rpexp12i  10534