Theorem simp-5l 549

Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)

Assertion

Ref	Expression
simp-5l	⊢ ((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜑)

Proof of Theorem simp-5l

Step	Hyp	Ref	Expression
1		simp-4l 547	. 2 ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)
2	1	adantr 276	1 ⊢ ((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜑)

This proof depends on syntax axioms:   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  simp-6l  551  aptap  8979  xaddf  10248  nn0ltexp2  11149  xrmaxiflemlub  12016  dfgcd2  12793  ctiunctlemfo  13332  mhmmnd  13921  neitx  15371  limccnp2cntop  15780  limccoap  15781  lgsval  16135