Theorem pm2.65i 135

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.1	. 2 |- (ph -> ps)
2		pm2.65i.2	. 2 |- (ph -> -. ps)
3		pm2.65 134	. 2 |- ((ph -> ps) -> ((ph -> -. ps) -> -. ph))
4	1, 2, 3	mp2 43	1 |- -. ph

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  canth 3913  cardprc 4872  nvex 8226

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

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