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Theorem ad5ant12 746
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant2.1 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
ad5ant12 (((((𝜑𝜓) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant12
StepHypRef Expression
1 ad5ant2.1 . 2 ((𝜑𝜓) → 𝜒)
21ad3antrrr 720 1 (((((𝜑𝜓) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 386
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 199  df-an 387
This theorem is referenced by:  simp-4r  774  fpwwe2  9802  lo1bdd2  14672  funcpropd  16956  curf2ndf  17284  metcnp3  22764  hoidmvle  41755  isomuspgrlem1  42754
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