Theorem 3bitr4rd 553

Description: Deduction from transitivity of biconditional.

Hypotheses

Ref	Expression
3bitr4d.1	|- (ph -> (ps <-> ch))
3bitr4d.2	|- (ph -> (th <-> ps))
3bitr4d.3	|- (ph -> (ta <-> ch))

Assertion

Ref	Expression
3bitr4rd	|- (ph -> (ta <-> th))

Proof of Theorem 3bitr4rd

Step	Hyp	Ref	Expression
1		3bitr4d.3	. . 3 |- (ph -> (ta <-> ch))
2		3bitr4d.1	. . 3 |- (ph -> (ps <-> ch))
3	1, 2	bitr4d 533	. 2 |- (ph -> (ta <-> ps))
4		3bitr4d.2	. 2 |- (ph -> (th <-> ps))
5	3, 4	bitr4d 533	1 |- (ph -> (ta <-> th))

Syntax hints:   -> wi 3   <-> wb 146

This theorem is referenced by:  oacan 4188  genpass 5124  lemuldivt 5876  lemuldivtOLD 5877  nn0ltlem1t 6131  climabs0 7113  iserzshft 7144  lmss 7950  causs 7952  sinperlem2 8682  dmdmdt 10222  cnvhmph 10513

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

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