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  7749  mulassnqg  7751  prarloc  7870  ltpopr  7962  ltexprlemfl  7976  ltexprlemfu  7978  addasssrg  8123  axaddass  8239  apmul1  9120  ltmul2  9188  lemul2  9189  dvdscmulr  12603  dvdsmulcr  12604  modremain  12712  ndvdsadd  12714  rpexp12i  12950  xblcntrps  15563  xblcntr  15564