Theorem exlimi 1463

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 1389	. 2 ⊢ (ψ → ∀xψ)
3		exlimi.2	. 2 ⊢ (φ → ψ)
4	2, 3	exlimih 1462	1 ⊢ (∃xφ → ψ)

Syntax hints:   → wi 4  Ⅎwnf 1325  ∃wex 1358

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-gen 1314  ax-ie2 1360  ax-4 1377

This theorem depends on definitions:  df-bi 110  df-nf 1326

This theorem is referenced by:  19.36i  1540  euexex  1963  ceqsex  2565  sbhypf  2576  vtoclgf  2585  vtoclef  2599  copsexg  3951  copsex2g  3953  ralxpf  4405  rexxpf  4406  dmcoss  4524  fv3  5118  tz6.12c  5124  0neqopab  5469  bj-exlimmpi  7156