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  6335  rexdif1en  9199  php  9248  fpwwe2lem4  10675  elfzoextl  13761  rprmdvdspow  33562  rprmdvdsprod  33563  constrmon  33786  aks4d1p3  42080  primrootsunit1  42099  primrootlekpowne0  42107  sticksstones1  42148  sticksstones11  42158  unitscyglem2  42198  uspgrimprop  47878