Theorem pm5.21ni 503

Description: Two propositions implying a false one are equivalent.

Hypotheses

Ref	Expression
pm5.21ni.1	|- (ph -> ps)
pm5.21ni.2	|- (ch -> ps)

Assertion

Ref	Expression
pm5.21ni	|- (-. ps -> (ph <-> ch))

Proof of Theorem pm5.21ni

Step	Hyp	Ref	Expression
1		pm5.21 502	. 2 |- ((-. ph /\ -. ch) -> (ph <-> ch))
2		pm5.21ni.1	. . 3 |- (ph -> ps)
3	2	con3i 90	. 2 |- (-. ps -> -. ph)
4		pm5.21ni.2	. . 3 |- (ch -> ps)
5	4	con3i 90	. 2 |- (-. ps -> -. ch)
6	1, 3, 5	sylanc 361	1 |- (-. ps -> (ph <-> ch))

Syntax hints:  -. wn 1   -> wi 2   <-> wb 127

This theorem is referenced by:  pm5.21nii 504  niabn 566  ordsucelsuc 2324  fvelrn 2883  ndmord 3064  breng 3280  brdomg 3281  r1pw 3529  r1pwcl 3530  alephsucdom 3685

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

This theorem depends on definitions:  df-bi 128  df-an 198

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