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Theorem adantrrr 478
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)
Hypothesis
Ref Expression
adantr2.1 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
adantrrr ((𝜑 ∧ (𝜓 ∧ (𝜒𝜏))) → 𝜃)

Proof of Theorem adantrrr
StepHypRef Expression
1 simpl 108 . 2 ((𝜒𝜏) → 𝜒)
2 adantr2.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylanr2 402 1 ((𝜑 ∧ (𝜓 ∧ (𝜒𝜏))) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  2ndconst  6087  genpdisj  7299  ltexprlemdisj  7382  addsrmo  7519  mulsrmo  7520  axpre-suploclemres  7677  lemul12b  8587  tgcl  12160  neissex  12261
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