Theorem 3adant3r 1262

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 1235	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1258	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1235	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1005

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 1007

This theorem is referenced by:  addassnqg  7662  mulassnqg  7664  prarloc  7783  ltpopr  7875  ltexprlemfl  7889  ltexprlemfu  7891  addasssrg  8036  axaddass  8152  apmul1  9027  ltmul2  9095  lemul2  9096  dvdscmulr  12461  dvdsmulcr  12462  modremain  12570  ndvdsadd  12572  rpexp12i  12807  xblcntrps  15224  xblcntr  15225