Theorem 19.21bi 1758

Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
19.21bi.1	⊢ (φ → ∀xψ)

Assertion

Ref	Expression
19.21bi	⊢ (φ → ψ)

Proof of Theorem 19.21bi

Step	Hyp	Ref	Expression
1		19.21bi.1	. 2 ⊢ (φ → ∀xψ)
2		sp 1747	. 2 ⊢ (∀xψ → ψ)
3	1, 2	syl 15	1 ⊢ (φ → ψ)

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  19.21bbi  1865  eqeq1  2359  eleq2  2414  r19.21bi  2713  ssel  3268  copsex2t  4609  funun  5147  fvopab4t  5386