Theorem 3adant3r 1132

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 1109	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1128	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1109	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  addassnqg  6480  mulassnqg  6482  prarloc  6601  ltpopr  6693  ltexprlemfl  6707  ltexprlemfu  6709  addasssrg  6841  axaddass  6946  apmul1  7764  ltmul2  7822  lemul2  7823