Theorem 3adant3r 1266

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 1239	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1262	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1239	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1009

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 1011

This theorem is referenced by:  addassnqg  7739  mulassnqg  7741  prarloc  7860  ltpopr  7952  ltexprlemfl  7966  ltexprlemfu  7968  addasssrg  8113  axaddass  8229  apmul1  9108  ltmul2  9176  lemul2  9177  dvdscmulr  12565  dvdsmulcr  12566  modremain  12674  ndvdsadd  12676  rpexp12i  12911  xblcntrps  15437  xblcntr  15438