Theorem 3adant3r 1261

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 1234	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1257	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1234	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1004

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 1006

This theorem is referenced by:  addassnqg  7602  mulassnqg  7604  prarloc  7723  ltpopr  7815  ltexprlemfl  7829  ltexprlemfu  7831  addasssrg  7976  axaddass  8092  apmul1  8968  ltmul2  9036  lemul2  9037  dvdscmulr  12399  dvdsmulcr  12400  modremain  12508  ndvdsadd  12510  rpexp12i  12745  xblcntrps  15156  xblcntr  15157