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Theorem 3adantr3 1051
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
Hypothesis
Ref Expression
3adantr.1 ((φ (ψ χ)) → θ)
Assertion
Ref Expression
3adantr3 ((φ (ψ χ τ)) → θ)

Proof of Theorem 3adantr3
StepHypRef Expression
1 3simpa 887 . 2 ((ψ χ τ) → (ψ χ))
2 3adantr.1 . 2 ((φ (ψ χ)) → θ)
31, 2sylan2 270 1 ((φ (ψ χ τ)) → θ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   w3a 871
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 873
This theorem is referenced by:  3ad2antr1  1055  3ad2antr2  1056  3adant3r3  1099  isosolem  5384  caovlem2d  5612
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