Theorem ibibr 593

Description: Implication in terms of implication and biconditional.

Assertion

Ref	Expression
ibibr	|- ((ph -> ps) <-> (ph -> (ps <-> ph)))

Proof of Theorem ibibr

Step	Hyp	Ref	Expression
1		ibib 592	. 2 |- ((ph -> ps) <-> (ph -> (ph <-> ps)))
2		bicom 522	. . 3 |- ((ph <-> ps) <-> (ps <-> ph))
3	2	imbi2i 185	. 2 |- ((ph -> (ph <-> ps)) <-> (ph -> (ps <-> ph)))
4	1, 3	bitr 173	1 |- ((ph -> ps) <-> (ph -> (ps <-> ph)))

Syntax hints:   -> wi 3   <-> wb 146

This theorem is referenced by:  oibabs 656  elab3g 1905  rabxfr 2908

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain