Theorem 3adant3r 1236

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 1209	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1232	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1209	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 979

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 981

This theorem is referenced by:  addassnqg  7394  mulassnqg  7396  prarloc  7515  ltpopr  7607  ltexprlemfl  7621  ltexprlemfu  7623  addasssrg  7768  axaddass  7884  apmul1  8758  ltmul2  8826  lemul2  8827  dvdscmulr  11840  dvdsmulcr  11841  modremain  11947  ndvdsadd  11949  rpexp12i  12168  xblcntrps  14153  xblcntr  14154