Theorem pm2.65d 136

Description: Deduction rule for proof by contradiction.

Hypotheses

Ref	Expression
pm2.65d.1	|- (ph -> (ps -> ch))
pm2.65d.2	|- (ph -> (ps -> -. ch))

Assertion

Ref	Expression
pm2.65d	|- (ph -> -. ps)

Proof of Theorem pm2.65d

Step	Hyp	Ref	Expression
1		pm2.65 134	. 2 |- ((ps -> ch) -> ((ps -> -. ch) -> -. ps))
2		pm2.65d.1	. 2 |- (ph -> (ps -> ch))
3		pm2.65d.2	. 2 |- (ph -> (ps -> -. ch))
4	1, 2, 3	sylc 68	1 |- (ph -> -. ps)

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  condan 480  cardlim 4862  climge0 7112  ivthlem7 7287  bl2in 7840  nmlno0lem 8449  nmlnop0ALT 9915

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

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