Theorem 2falsed 710

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 624	. 2 |- ( ph -> ( ps -> ch ) )
3		2falsed.2	. . 3 |- ( ph -> -. ch )
4	3	pm2.21d 624	. 2 |- ( ph -> ( ch -> ps ) )
5	2, 4	impbid 129	1 |- ( ph -> ( ps <-> ch ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108  ax-in2 620

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm5.21ni  711  bianfd  957  abvor0dc  3520  nn0eln0  4724  nntri3  6708  fin0  7117  omp1eomlem  7336  ctssdccl  7353  ismkvnex  7397  xrlttri3  10076  nltpnft  10093  ngtmnft  10096  xrrebnd  10098  xltadd1  10155  xposdif  10161  xleaddadd  10166  xqltnle  10573  hashnncl  11103  zfz1isolemiso  11149  mod2eq1n2dvds  12503  m1exp1  12525  bitsmod  12580  pceq0  12958  2omap  16698