Theorem bijust 175

Description: Theorem used to justify definition of biconditional df-bi 177. (Contributed by NM, 11-May-1999.) (Proof shortened by Josh Purinton, 29-Dec-2000.)

Assertion

Ref	Expression
bijust	|- -. ((-. ((ph -> ps) -> -. (ps -> ph)) -> -. ((ph -> ps) -> -. (ps -> ph))) -> -. (-. ((ph -> ps) -> -. (ps -> ph)) -> -. ((ph -> ps) -> -. (ps -> ph))))

Proof of Theorem bijust

Step	Hyp	Ref	Expression
1		id 19	. 2 |- (-. ((ph -> ps) -> -. (ps -> ph)) -> -. ((ph -> ps) -> -. (ps -> ph)))
2		pm2.01 160	. 2 |- (((-. ((ph -> ps) -> -. (ps -> ph)) -> -. ((ph -> ps) -> -. (ps -> ph))) -> -. (-. ((ph -> ps) -> -. (ps -> ph)) -> -. ((ph -> ps) -> -. (ps -> ph)))) -> -. (-. ((ph -> ps) -> -. (ps -> ph)) -> -. ((ph -> ps) -> -. (ps -> ph))))
3	1, 2	mt2 170	1 |- -. ((-. ((ph -> ps) -> -. (ps -> ph)) -> -. ((ph -> ps) -> -. (ps -> ph))) -> -. (-. ((ph -> ps) -> -. (ps -> ph)) -> -. ((ph -> ps) -> -. (ps -> ph))))

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: (None)