Theorem pm5.4 184

Description: Antecedent absorption implication. Theorem *5.4 of [WhiteheadRussell] p. 125.

Assertion

Ref	Expression
pm5.4	|- ((ph -> (ph -> ps)) <-> (ph -> ps))

Proof of Theorem pm5.4

Step	Hyp	Ref	Expression
1		pm2.43 77	. 2 |- ((ph -> (ph -> ps)) -> (ph -> ps))
2		ax-1 4	. 2 |- ((ph -> ps) -> (ph -> (ph -> ps)))
3	1, 2	impbii 174	1 |- ((ph -> (ph -> ps)) <-> (ph -> ps))

Syntax hints:   -> wi 3   <-> wb 163

This theorem is referenced by:  pm4.78 381  moabs 1811

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 164

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