Theorem abai 490

Description: Introduce one conjunct as an antecedent to the another.

Assertion

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

Proof of Theorem abai

Step	Hyp	Ref	Expression
1		pm3.26 326	. . 3 |- ((ph /\ ps) -> ph)
2		pm3.4 338	. . 3 |- ((ph /\ ps) -> (ph -> ps))
3	1, 2	jca 295	. 2 |- ((ph /\ ps) -> (ph /\ (ph -> ps)))
4		pm3.26 326	. . 3 |- ((ph /\ (ph -> ps)) -> ph)
5		pm3.35 366	. . 3 |- ((ph /\ (ph -> ps)) -> ps)
6	4, 5	jca 295	. 2 |- ((ph /\ (ph -> ps)) -> (ph /\ ps))
7	3, 6	impbii 164	1 |- ((ph /\ ps) <-> (ph /\ (ph -> ps)))

Syntax hints:   -> wi 3   <-> wb 153   /\ wa 230

This theorem is referenced by:  eu2 1438  euan 1470  2eu6 1497  r19.29 1803  dfss4 2293  difin 2296  tfrlem2 3970  choc0 9373

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 154  df-an 232

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