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Theorem 3ad2antl1 1065
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)
Hypothesis
Ref Expression
3ad2antl.1 ((φ χ) → θ)
Assertion
Ref Expression
3ad2antl1 (((φ ψ τ) χ) → θ)

Proof of Theorem 3ad2antl1
StepHypRef Expression
1 3ad2antl.1 . . 3 ((φ χ) → θ)
21adantlr 446 . 2 (((φ τ) χ) → θ)
323adantl2 1060 1 (((φ ψ τ) χ) → θ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   w3a 884
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 886
This theorem is referenced by:  acexmid  5454  addlocpr  6518  distrlem1prl  6557  distrlem1pru  6558  ltsopr  6569  addcanprlemu  6588  fzo1fzo0n0  8789  expival  8891
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