Theorem exlimi 1482

Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
exlimi.1	⊢ Ⅎxψ
exlimi.2	⊢ (φ → ψ)

Assertion

Ref	Expression
exlimi	⊢ (∃xφ → ψ)

Proof of Theorem exlimi

Step	Hyp	Ref	Expression
1		exlimi.1	. . 3 ⊢ Ⅎxψ
2	1	nfri 1409	. 2 ⊢ (ψ → ∀xψ)
3		exlimi.2	. 2 ⊢ (φ → ψ)
4	2, 3	exlimih 1481	1 ⊢ (∃xφ → ψ)

Syntax hints:   → wi 4  Ⅎwnf 1346  ∃wex 1378

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-gen 1335  ax-ie2 1380  ax-4 1397

This theorem depends on definitions:  df-bi 110  df-nf 1347

This theorem is referenced by:  19.36i  1559  euexex  1982  ceqsex  2586  sbhypf  2597  vtoclgf  2606  vtoclef  2620  copsexg  3972  copsex2g  3974  ralxpf  4425  rexxpf  4426  dmcoss  4544  fv3  5140  tz6.12c  5146  0neqopab  5492  bj-exlimmpi  9245