Theorem nbbn 724

Description: Move negation outside of biconditional. Compare Theorem *5.18 of [WhiteheadRussell] p. 124.

Assertion

Ref	Expression
nbbn	|- ((-. ph <-> ps) <-> -. (ph <-> ps))

Proof of Theorem nbbn

Step	Hyp	Ref	Expression
1		bicom 579	. 2 |- ((-. ph <-> ps) <-> (ps <-> -. ph))
2		bicom 579	. . . 4 |- ((ph <-> ps) <-> (ps <-> ph))
3		pm5.18 722	. . . 4 |- ((ps <-> ph) <-> -. (ps <-> -. ph))
4	2, 3	bitri 190	. . 3 |- ((ph <-> ps) <-> -. (ps <-> -. ph))
5	4	con2bii 238	. 2 |- ((ps <-> -. ph) <-> -. (ph <-> ps))
6	1, 5	bitri 190	1 |- ((-. ph <-> ps) <-> -. (ph <-> ps))

Syntax hints:  -. wn 2   <-> wb 163

This theorem is referenced by:  xor 734  biass 816  symdif2OLD 2858  canth 5112  TFBid 14121  assxor 14279

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

This theorem depends on definitions:  df-bi 164  df-an 242

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