Theorem sylnib 295

Description: A mixed syllogism inference from an implication and a biconditional. (Contributed by Wolf Lammen, 16-Dec-2013.)

Hypotheses

Ref	Expression
sylnib.1	|- (ph -> -. ps)
sylnib.2	|- (ps <-> ch)

Assertion

Ref	Expression
sylnib	|- (ph -> -. ch)

Proof of Theorem sylnib

Step	Hyp	Ref	Expression
1		sylnib.1	. 2 |- (ph -> -. ps)
2		sylnib.2	. . 3 |- (ps <-> ch)
3	2	a1i 10	. 2 |- (ph -> (ps <-> ch))
4	1, 3	mtbid 291	1 |- (ph -> -. ch)

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176

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 177

This theorem is referenced by:  sylnibr  296  ssnelpss  3614  nnc3n3p1  6279  nchoicelem1  6290