Theorem syldbl2 1333

Description: Stacked hypotheseis implies goal. (Contributed by Stanislas Polu, 9-Mar-2020.)

Hypothesis

Ref	Expression
syldbl2.1	⊢ ((𝜑 ∧ 𝜓) → (𝜓 → 𝜃))

Assertion

Ref	Expression
syldbl2	⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Proof of Theorem syldbl2

Step	Hyp	Ref	Expression
1		syldbl2.1	. . 3 ⊢ ((𝜑 ∧ 𝜓) → (𝜓 → 𝜃))
2	1	com12 30	. 2 ⊢ (𝜓 → ((𝜑 ∧ 𝜓) → 𝜃))
3	2	anabsi7 587	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃)

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 proof depends on definitions:  df-bi 117

This theorem is used by:  reldmm  5000  elfzoextl  10609