Theorem 3adant3r2 1244

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 17-Feb-2008.)

Hypothesis

Ref	Expression
3exp.1	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
3adant3r2	|- ( ( ph /\ ( ps /\ ta /\ ch ) ) -> th )

Proof of Theorem 3adant3r2

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3expb 1235	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3adantr2 1188	1 |- ( ( ph /\ ( ps /\ ta /\ ch ) ) -> 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:  grppnpcan2  13952  mulgsubdir  14018  imasrng  14339  imasring  14453  opprring  14468  mettri2  15554  mettri  15565  xmetrtri  15568