Theorem 3adant2r 855

Description: Deduction adding a conjunct to antecedent.

Hypothesis

Ref	Expression
3adant1l.1	|- ((ph /\ ps /\ ch) -> th)

Assertion

Ref	Expression
3adant2r	|- ((ph /\ (ps /\ ta) /\ ch) -> th)

Proof of Theorem 3adant2r

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 |- ((ph /\ ps /\ ch) -> th)
2	1	3com12 837	. . 3 |- ((ps /\ ph /\ ch) -> th)
3	2	3adant1r 853	. 2 |- (((ps /\ ta) /\ ph /\ ch) -> th)
4	3	3com12 837	1 |- ((ph /\ (ps /\ ta) /\ ch) -> th)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 775

This theorem is referenced by:  lt2mul2divt 5872  ssbl 7855  nvaddsub4 8281  nmoub2i 8437

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 777

Copyright terms: Public domain