Theorem pm2.01bd 14274

Description: Deduction based on reductio ad absurdum. (The proof was shortened by Andrew Salmon, 7-May-2011.)

Hypothesis

Ref	Expression
pm2.01bd.1	|- (ph -> (-. ps -> ps))

Assertion

Ref	Expression
pm2.01bd	|- (ph -> ps)

Proof of Theorem pm2.01bd

Step	Hyp	Ref	Expression
1		pm2.01bd.1	. 2 |- (ph -> (-. ps -> ps))
2		pm2.18 97	. 2 |- ((-. ps -> ps) -> ps)
3	1, 2	syl 12	1 |- (ph -> ps)

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  isunscov 14386  bwt2 14960

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

Copyright terms: Public domain