Theorem exlimivOLD 1698

Description: Obsolete version of exlimiv 1634 as of 4-Dec-2017. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
exlimivOLD.1	⊢ (φ → ψ)

Assertion

Ref	Expression
exlimivOLD	⊢ (∃xφ → ψ)

Distinct variable group:   ψ,x

Allowed substitution hint:   φ(x)

Proof of Theorem exlimivOLD

Step	Hyp	Ref	Expression
1		exlimivOLD.1	. . 3 ⊢ (φ → ψ)
2	1	eximi 1576	. 2 ⊢ (∃xφ → ∃xψ)
3		19.9v 1664	. 2 ⊢ (∃xψ ↔ ψ)
4	2, 3	sylib 188	1 ⊢ (∃xφ → ψ)

Syntax hints:   → wi 4  ∃wex 1541

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

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by: (None)