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Theorem al2imi 1344
Description: Inference quantifying antecedent, nested antecedent, and consequent. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
al2imi.1 (φ → (ψχ))
Assertion
Ref Expression
al2imi (xφ → (xψxχ))

Proof of Theorem al2imi
StepHypRef Expression
1 al2imi.1 . . 3 (φ → (ψχ))
21alimi 1341 . 2 (xφx(ψχ))
3 alim 1343 . 2 (x(ψχ) → (xψxχ))
42, 3syl 14 1 (xφ → (xψxχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1333  ax-gen 1335
This theorem is referenced by:  alanimi  1345  alimdh  1353  albi  1354  19.30dc  1515  19.33b2  1517  hbnt  1540  ax10o  1600  spimth  1620  sbi1v  1768  ralim  2374  ceqsalt  2574  intss  3627
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