Theorem ad5ant12 754

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)

Hypothesis

Ref	Expression
ad5ant2.1	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Assertion

Ref	Expression
ad5ant12	⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant12

Step	Hyp	Ref	Expression
1		ad5ant2.1	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
2	1	ad3antrrr 728	1 ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 396

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 206  df-an 397

This theorem is referenced by:  fpwwe2  10640  swrdccatin1  14679  lo1bdd2  15472  funcpropd  17855  curf2ndf  18204  metcnp3  24269  perpneq  28220  nsgmgc  32785  fmla1  34664  omabs2  42384  fnchoice  44015  hoidmvle  45615  isomuspgrlem1  46794