Theorem 2falsed 703

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 620	. 2 |- ( ph -> ( ps -> ch ) )
3		2falsed.2	. . 3 |- ( ph -> -. ch )
4	3	pm2.21d 620	. 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 616

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm5.21ni  704  bianfd  950  abvor0dc  3471  nn0eln0  4653  nntri3  6552  fin0  6943  omp1eomlem  7155  ctssdccl  7172  ismkvnex  7216  xrlttri3  9866  nltpnft  9883  ngtmnft  9886  xrrebnd  9888  xltadd1  9945  xposdif  9951  xleaddadd  9956  xqltnle  10339  hashnncl  10869  zfz1isolemiso  10913  mod2eq1n2dvds  12023  m1exp1  12045  pceq0  12463