Theorem biantr 742

Description: A transitive law of equivalence. Compare Theorem *4.22 of [WhiteheadRussell] p. 117.

Assertion

Ref	Expression
biantr	|- (((ph <-> ps) /\ (ch <-> ps)) -> (ph <-> ch))

Proof of Theorem biantr

Step	Hyp	Ref	Expression
1		id 59	. . 3 |- ((ch <-> ps) -> (ch <-> ps))
2	1	bibi2d 618	. 2 |- ((ch <-> ps) -> ((ph <-> ch) <-> (ph <-> ps)))
3	2	biimparc 419	1 |- (((ph <-> ps) /\ (ch <-> ps)) -> (ph <-> ch))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223

This theorem is referenced by:  bm1.1 1462

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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