Theorem 19.36aiv 1826

Description: Inference from Theorem 19.36 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
19.36aiv.1	⊢ ∃𝑥(𝜑 → 𝜓)

Assertion

Ref	Expression
19.36aiv	⊢ (∀𝑥𝜑 → 𝜓)

Distinct variable group:   𝜓,𝑥

Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem 19.36aiv

Step	Hyp	Ref	Expression
1		nfv 1464	. 2 ⊢ Ⅎ𝑥𝜓
2		19.36aiv.1	. 2 ⊢ ∃𝑥(𝜑 → 𝜓)
3	1, 2	19.36i 1605	1 ⊢ (∀𝑥𝜑 → 𝜓)

Syntax hints:   → wi 4  ∀wal 1285  ∃wex 1424

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-17 1462  ax-ial 1470

This theorem depends on definitions:  df-bi 115  df-nf 1393

This theorem is referenced by:  vtocl2  2668  vtocl3  2669