Theorem con4d 97

Description: Deduction derived from Axiom ax-3 8. (Contributed by NM, 26-Mar-1995.)

Hypothesis

Ref	Expression
con4d.1	|- (ph -> (-. ps -> -. ch))

Assertion

Ref	Expression
con4d	|- (ph -> (ch -> ps))

Proof of Theorem con4d

Step	Hyp	Ref	Expression
1		con4d.1	. 2 |- (ph -> (-. ps -> -. ch))
2		ax-3 8	. 2 |- ((-. ps -> -. ch) -> (ch -> ps))
3	1, 2	syl 15	1 |- (ph -> (ch -> ps))

Syntax hints:  -. wn 3   -> wi 4

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

This theorem is referenced by:  pm2.21d  98  pm2.18  102  con2d  107  con1d  116  mt4d  130  impcon4bid  196  con4bid  284  exim  1575  sp  1747  spOLD  1748  axi11e  2332  necon2ad  2565  spc2gv  2943  spc3gv  2945  addceq0  6220