Theorem elv 33983

Description: New way (elv 33983, el2v 33984 theorems and el3v 33987 theorems) to shorten some proofs. Inference forms (with 𝐴 ∈ V hypotheses) of the general theorems (proving 𝐴 ∈ 𝑉 →) may be superfluous. (Contributed by Peter Mazsa, 13-Oct-2018.)

Hypothesis

Ref	Expression
elv.1	⊢ (𝑥 ∈ V → 𝜑)

Assertion

Ref	Expression
elv	⊢ 𝜑

Proof of Theorem elv

Step	Hyp	Ref	Expression
1		vex 3203	. 2 ⊢ 𝑥 ∈ V
2		elv.1	. 2 ⊢ (𝑥 ∈ V → 𝜑)
3	1, 2	ax-mp 5	1 ⊢ 𝜑

Syntax hints:   → wi 4   ∈ wcel 1990  Vcvv 3200

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-12 2047  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1486  df-ex 1705  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-v 3202

This theorem is referenced by:  eldmres  34036  ecres  34043  ecres2  34044  eldmqsres  34051  inxprnres  34060  cnvepres  34066  idinxpss  34083  inxpssidinxp  34086  idinxpssinxp  34087  alrmomo  34123  alrmomo2  34124