Theorem 2falsed 651

Description: Two falsehoods are equivalent (deduction rule). (Contributed by NM, 11-Oct-2013.)

Hypotheses

Ref	Expression
2falsed.1	|- ( ph -> -. ps )
2falsed.2	|- ( ph -> -. ch )

Assertion

Ref	Expression
2falsed	|- ( ph -> ( ps <-> ch ) )

Proof of Theorem 2falsed

Step	Hyp	Ref	Expression
1		2falsed.1	. . 3 |- ( ph -> -. ps )
2	1	pm2.21d 582	. 2 |- ( ph -> ( ps -> ch ) )
3		2falsed.2	. . 3 |- ( ph -> -. ch )
4	3	pm2.21d 582	. 2 |- ( ph -> ( ch -> ps ) )
5	2, 4	impbid 127	1 |- ( ph -> ( ps <-> ch ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-ia3 106  ax-in2 578

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm5.21ni  652  bianfd  890  abvor0dc  3285  nn0eln0  4387  nntri3  6161  fin0  6441  xrlttri3  9000  nltpnft  9012  ngtmnft  9013  xrrebnd  9014  hashnncl  9872  mod2eq1n2dvds  10486  m1exp1  10508