Theorem pm2.65i 116

Description: Inference rule for proof by contradiction.

Hypotheses

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

Assertion

Ref	Expression
pm2.65i	|- -. ph

Proof of Theorem pm2.65i

Step	Hyp	Ref	Expression
1		pm2.65i.2	. . 3 |- (ph -> -. ps)
2		pm2.65i.1	. . 3 |- (ph -> ps)
3	1, 2	nsyl 102	. 2 |- (ph -> -. ph)
4		pm2.01 80	. 2 |- ((ph -> -. ph) -> -. ph)
5	3, 4	ax-mp 6	1 |- -. ph

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  canth 2945  cardprc 3667

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

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