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Theorem r19.29anOLD 3295
 Description: Obsolete version of r19.29an 3253 as of 17-Jun-2023. (Contributed by Thierry Arnoux, 29-Dec-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
r19.29anOLD.1 (((𝜑𝑥𝐴) ∧ 𝜓) → 𝜒)
Assertion
Ref Expression
r19.29anOLD ((𝜑 ∧ ∃𝑥𝐴 𝜓) → 𝜒)
Distinct variable groups:   𝜒,𝑥   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝐴(𝑥)

Proof of Theorem r19.29anOLD
StepHypRef Expression
1 nfv 1896 . . 3 𝑥𝜑
2 nfre1 3271 . . 3 𝑥𝑥𝐴 𝜓
31, 2nfan 1885 . 2 𝑥(𝜑 ∧ ∃𝑥𝐴 𝜓)
4 r19.29anOLD.1 . . 3 (((𝜑𝑥𝐴) ∧ 𝜓) → 𝜒)
54adantllr 715 . 2 ((((𝜑 ∧ ∃𝑥𝐴 𝜓) ∧ 𝑥𝐴) ∧ 𝜓) → 𝜒)
6 simpr 485 . 2 ((𝜑 ∧ ∃𝑥𝐴 𝜓) → ∃𝑥𝐴 𝜓)
73, 5, 6r19.29af 3294 1 ((𝜑 ∧ ∃𝑥𝐴 𝜓) → 𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 396   ∈ wcel 2083  ∃wrex 3108 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1781  ax-4 1795  ax-5 1892  ax-6 1951  ax-7 1996  ax-10 2114  ax-12 2143 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1528  df-ex 1766  df-nf 1770  df-ral 3112  df-rex 3113 This theorem is referenced by: (None)
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