Theorem 3anidm12 882

Description: Inference from idempotent law for conjunction.

Hypothesis

Ref	Expression
3anidm12.1	|- ((ph /\ ph /\ ps) -> ch)

Assertion

Ref	Expression
3anidm12	|- ((ph /\ ps) -> ch)

Proof of Theorem 3anidm12

Step	Hyp	Ref	Expression
1		3anidm12.1	. . . 4 |- ((ph /\ ph /\ ps) -> ch)
2	1	3exp 832	. . 3 |- (ph -> (ph -> (ps -> ch)))
3	2	pm2.43i 64	. 2 |- (ph -> (ps -> ch))
4	3	imp 350	1 |- ((ph /\ ps) -> ch)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 775

This theorem is referenced by:  3anidm13 883  dividt 5766  qrecclt 6273  subsqt 6642  fsum0split 7021  abscncflem 7274  metidcn 7900  ablnncan 8112  kbpjt 9880

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  df-3an 777

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