Theorem 2thd 231

Description: Two truths are equivalent (deduction rule). (Contributed by NM, 3-Jun-2012.)

Hypotheses

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

Assertion

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

Proof of Theorem 2thd

Step	Hyp	Ref	Expression
1		2thd.1	. 2 |- (ph -> ps)
2		2thd.2	. 2 |- (ph -> ch)
3		pm5.1im 229	. 2 |- (ps -> (ch -> (ps <-> ch)))
4	1, 2, 3	sylc 56	1 |- (ph -> (ps <-> ch))

Syntax hints:   -> wi 4   <-> wb 176

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  had1  1402  sbc2or  3054  abvor0  3567  ralidm  3653  fcnvres  5243