Theorem biantr 556

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 9	. . 3 |- ((ch <-> ps) -> (ch <-> ps))
2	1	bibi2d 470	. 2 |- ((ch <-> ps) -> ((ph <-> ch) <-> (ph <-> ps)))
3	2	biimparc 327	1 |- (((ph <-> ps) /\ (ch <-> ps)) -> (ph <-> ch))

Syntax hints:   -> wi 2   <-> wb 127   /\ wa 196

This theorem is referenced by:  bm1.1 1088

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

This theorem depends on definitions:  df-bi 128  df-an 198

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