Theorem ahypfmbi 10421

Description: Add a hypothesis into the first member of a biimplication.

Hypothesis

Ref	Expression
ahypfmbi.1	|- (ps <-> ch)

Assertion

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

Proof of Theorem ahypfmbi

Step	Hyp	Ref	Expression
1		ahypfmbi.1	. . 3 |- (ps <-> ch)
2	1	anbi2i 482	. 2 |- ((ph /\ ps) <-> (ph /\ ch))
3	2	baib 687	1 |- (ph -> ((ph /\ ps) <-> ch))

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

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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