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 )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  addassnqg  7750  mulassnqg  7752  prarloc  7871  ltpopr  7963  ltexprlemfl  7977  ltexprlemfu  7979  addasssrg  8124  axaddass  8240  apmul1  9121  ltmul2  9189  lemul2  9190  dvdscmulr  12606  dvdsmulcr  12607  modremain  12715  ndvdsadd  12717  rpexp12i  12953  xblcntrps  15605  xblcntr  15606