Theorem 2falsed 697

Description: Two falsehoods are equivalent (deduction form). (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 614	. 2 |- ( ph -> ( ps -> ch ) )
3		2falsed.2	. . 3 |- ( ph -> -. ch )
4	3	pm2.21d 614	. 2 |- ( ph -> ( ch -> ps ) )
5	2, 4	impbid 128	1 |- ( ph -> ( ps <-> ch ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107  ax-in2 610

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm5.21ni  698  bianfd  943  abvor0dc  3437  nn0eln0  4602  nntri3  6474  fin0  6861  omp1eomlem  7069  ctssdccl  7086  ismkvnex  7129  xrlttri3  9747  nltpnft  9764  ngtmnft  9767  xrrebnd  9769  xltadd1  9826  xposdif  9832  xleaddadd  9837  hashnncl  10723  zfz1isolemiso  10767  mod2eq1n2dvds  11831  m1exp1  11853  pceq0  12268