Theorem 3bitr3g 554

Description: More general version of 3bitr3 181. Useful for converting definitions in a formula.

Hypotheses

Ref	Expression
3bitr3g.1	|- (ph -> (ps <-> ch))
3bitr3g.2	|- (ps <-> th)
3bitr3g.3	|- (ch <-> ta)

Assertion

Ref	Expression
3bitr3g	|- (ph -> (th <-> ta))

Proof of Theorem 3bitr3g

Step	Hyp	Ref	Expression
1		3bitr3g.1	. . 3 |- (ph -> (ps <-> ch))
2		3bitr3g.2	. . 3 |- (ps <-> th)
3	1, 2	syl5bbr 534	. 2 |- (ph -> (th <-> ch))
4		3bitr3g.3	. 2 |- (ch <-> ta)
5	3, 4	syl6bb 536	1 |- (ph -> (th <-> ta))

Syntax hints:   -> wi 3   <-> wb 146

This theorem is referenced by:  unineq 2255  elsncg 2430  iununi 2616  erth 4282  ereldm 4285  cardeq0 4832  axpownd 4953  suplem2pr 5162  lt2msq 5881

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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