Theorem 3o3cs 29311

Description: Deduction eliminating disjunct. (Contributed by Thierry Arnoux, 19-Dec-2016.)

Hypothesis

Ref	Expression
3o1cs.1	|- ( ( ph \/ ps \/ ch ) -> th )

Assertion

Ref	Expression
3o3cs	|- ( ch -> th )

Proof of Theorem 3o3cs

Step	Hyp	Ref	Expression
1		df-3or 1038	. . 3 |- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
2		3o1cs.1	. . 3 |- ( ( ph \/ ps \/ ch ) -> th )
3	1, 2	sylbir 225	. 2 |- ( ( ( ph \/ ps ) \/ ch ) -> th )
4	3	olcs 410	1 |- ( ch -> th )

Syntax hints:   -> wi 4   \/ wo 383   \/ w3o 1036

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-3or 1038

This theorem is referenced by:  xrpxdivcld  29643