Theorem ad5ant12 755

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 729	1 ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395

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 207  df-an 396

This theorem is referenced by:  fpwwe2  10712  swrdccatin1  14773  lo1bdd2  15570  funcpropd  17967  curf2ndf  18317  metcnp3  24574  perpneq  28740  rloccring  33242  nsgmgc  33405  drngmxidlr  33471  fmla1  35355  omabs2  43294  fnchoice  44929  hoidmvle  46521  isuspgrimlem  47758