Theorem a4w 929

Description: A weaker version of a4c 843.

Hypothesis

Ref	Expression
a4w.1	⊢ (x = y → (φ → ψ))

Assertion

Ref	Expression
a4w	⊢ (φ → ∃xψ)

Distinct variable group(s):   φ,x

Proof of Theorem a4w

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 ⊢ (φ → ∀xφ)
2		a4w.1	. 2 ⊢ (x = y → (φ → ψ))
3	1, 2	a4c 843	1 ⊢ (φ → ∃xψ)

Syntax hints:   → wi 2  ∃wex 678   = weq 797

This theorem is referenced by:  a4w1 930  zfpair 1891

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-9 799  ax-17 925

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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