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Theorem 3adant1l 1193
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant1l (((𝜏𝜑) ∧ 𝜓𝜒) → 𝜃)

Proof of Theorem 3adant1l
StepHypRef Expression
1 3adant1l.1 . . . 4 ((𝜑𝜓𝜒) → 𝜃)
213expb 1167 . . 3 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
32adantll 467 . 2 (((𝜏𝜑) ∧ (𝜓𝜒)) → 𝜃)
433impb 1162 1 (((𝜏𝜑) ∧ 𝜓𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 947
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 depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by:  3adant2l  1195  3adant3l  1197  tfrcl  6229  addassnqg  7158  mulassnqg  7160  addasssrg  7532  axaddass  7648
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