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Theorem 3anim123i 1137
 Description: Join antecedents and consequents with conjunction. (Contributed by NM, 8-Apr-1994.)
Hypotheses
Ref Expression
3anim123i.1 (φψ)
3anim123i.2 (χθ)
3anim123i.3 (τη)
Assertion
Ref Expression
3anim123i ((φ χ τ) → (ψ θ η))

Proof of Theorem 3anim123i
StepHypRef Expression
1 3anim123i.1 . . 3 (φψ)
213ad2ant1 976 . 2 ((φ χ τ) → ψ)
3 3anim123i.2 . . 3 (χθ)
433ad2ant2 977 . 2 ((φ χ τ) → θ)
5 3anim123i.3 . . 3 (τη)
653ad2ant3 978 . 2 ((φ χ τ) → η)
72, 4, 63jca 1132 1 ((φ χ τ) → (ψ θ η))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 934 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936 This theorem is referenced by:  3anim1i  1138  3anim3i  1139  syl3an  1224  syl3anl  1233  spc3egv  2943
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