Theorem syldbl2 841

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 32	. 2 ⊢ (𝜓 → ((𝜑 ∧ 𝜓) → 𝜃))
3	2	anabsi7 671	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃)

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:  elpredimg  6268  rexdif1en  9082  php  9131  fpwwe2lem4  10547  elfzoextl  13642  rprmdvdspow  33480  rprmdvdsprod  33481  constrmon  33710  aks4d1p3  42051  primrootsunit1  42070  primrootlekpowne0  42078  sticksstones1  42119  sticksstones11  42129  unitscyglem2  42169