Theorem pm5.74rd 590

Description: Distribution of implication over biconditional (deduction rule).

Hypothesis

Ref	Expression
pm5.74rd.1	|- (ph -> ((ps -> ch) <-> (ps -> th)))

Assertion

Ref	Expression
pm5.74rd	|- (ph -> (ps -> (ch <-> th)))

Proof of Theorem pm5.74rd

Step	Hyp	Ref	Expression
1		pm5.74rd.1	. 2 |- (ph -> ((ps -> ch) <-> (ps -> th)))
2		pm5.74 585	. 2 |- ((ps -> (ch <-> th)) <-> ((ps -> ch) <-> (ps -> th)))
3	1, 2	sylibr 200	1 |- (ph -> (ps -> (ch <-> th)))

Syntax hints:   -> wi 3   <-> wb 146

This theorem is referenced by:  pm5.35 684  sbc5g 1957  sbc6g 1958  sbcel1gv 1983  sbcel2gv 1984  nn1suc 5941

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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